Analysis strategies for high-resolution UHF-fMRI data

Abstract

Functional MRI (fMRI) benefits from both increased sensitivity and specificity with increasing magnetic field strength, making it a key application for Ultra-High Field (UHF) MRI scanners. Most UHF-fMRI studies utilize the dramatic increases in sensitivity and specificity to acquire high-resolution data reaching sub-millimeter scales, which enable new classes of experiments to probe the functional organization of the human brain. This review article surveys advanced data analysis strategies developed for high-resolution fMRI at UHF. These include strategies designed to mitigate distortion and artifacts associated with higher fields in ways that attempt to preserve spatial resolution of the fMRI data, as well as recently introduced analysis techniques that are enabled by these extremely high-resolution data. Particular focus is placed on anatomically-informed analyses, including cortical surface-based analysis, which are powerful techniques that can guide each step of the analysis from preprocessing to statistical analysis to interpretation and visualization. New intracortical analysis techniques for laminar and columnar fMRI are also reviewed and discussed. Prospects for single-subject individualized analyses are also presented and discussed. Altogether, there are both specific challenges and opportunities presented by UHF-fMRI, and the use of proper analysis strategies can help these valuable data reach their full potential.

1. INTRODUCTION

Functional MRI (fMRI) benefits enormously from the increased sensitivity afforded by ultra-high magnetic fields (≥ 7 Tesla) compared to conventional field strengths. While the higher main magnetic field strength acts to increase image signal-to-noise ratio (SNR) [Edelstein et al., 1986], contrast in T₂^*-based techniques such as blood oxygenation level dependent (BOLD) imaging is also enhanced at higher field strengths [Turner et al., 1993; Yacoub et al., 2001], giving rise to a substantial increase in functional contrast-to-noise ratio (fCNR). For this reason, fMRI has been a key application of Ultra-High Field MRI systems [see Uğurbil, this issue] and a primary motivation for pushing to even higher field strengths [see Budinger & Bird, this issue].

The increased sensitivity of UHF-fMRI compared to fMRI at conventional field strengths of 1.5 and 3 T can be utilized in several ways. The increased sensitivity can help to shorten scan times, since with higher fCNR subtle functional activation can be detected with fewer averages or in a reduced number of runs, leading to more time-efficient sessions—which is critical in the clinical setting or for certain patient populations. The sensitivity boost can also be exploited to include more runs in a single experimental session, allowing for multiple stimuli or tasks or for a richer set of accompanying anatomical data. By reducing the need to pool data across groups of subjects, the increased sensitivity can allow for single-subject studies and, perhaps eventually patient-specific diagnoses [Zarogianni et al., 2013; Arbabshirani et al., 2016]. However, the predominant use of this increased sensitivity has been to increase the spatiotemporal resolution of the acquisition [see Dumoulin et al. and De Martino et al., this issue]. Increasing spatial resolution reduces the voxel volume, and therefore incurs a cost of lowering image SNR through reducing random noise cancellation within the voxel. Increasing temporal resolution increases the sampling rate, and therefore incurs a cost of lowering image SNR through reducing signal recovery via longitudinal relaxation. UHF-fMRI provides the additional SNR needed to offset these costs and attain the desired high-resolution. Finer spatial sampling helps to resolve the cortical gray matter ribbon as well as small subcortical structures [Newton et al., 2012; De Martino et al., 2013a; Satpute et al., 2013; Faull et al., 2015], and faster sampling allows for adequate sampling of the rapid hemodynamic response to transient neuronal activity [Smith et al., 2013; Lewis et al., 2016]. High spatiotemporal resolution also enables strategies to adequately sample and avoid physiological noise sources, as described below. Overall, increased spatiotemporal resolution can both enable new investigations into the fine-scale organization of the brain and improve the neuronal specificity of the fMRI signals.

Despite the clear advantages provided by UHF, UHF-fMRI faces many challenges that must be addressed in order to reach the full potential that the boost in fCNR can provide. As field strength increases, field inhomogeneity—both in the local magnetic field B₀ due to increased magnetic susceptibility effects and in the radiofrequency transmit and receive fields B₁⁺ and B₁⁻ due to dielectric effects—can cause artifacts that partially diminish the gains achieved by imaging at higher field. These spatial inhomogeneities cause image artifacts such as geometric distortion and image intensity biases over the brain. They are also present at conventional field strengths but scale with field strength and are therefore more pronounced at UHF. While advanced acquisition techniques exist that can partially mitigate these artifacts [Setsompop et al., 2016], these more pronounced artifacts at UHF present specific challenges for UHF-fMRI analysis—especially for studies requiring the spatial accuracy expected from nominally high-resolution acquisitions. Indeed, there are many stages in conventional fMRI analysis streams that can introduce resolution loss or detection biases, and so specialized analysis strategies are called for to preserve the advantages afforded by UHF-fMRI.

This review focuses on fMRI analysis strategies developed for UHF. While many of these techniques were originally designed for UHF-fMRI, they can also be readily applied to fMRI data at conventional field strengths for studies employing high resolution acquisitions or those that require a high degree of spatial accuracy and/or a low degree of detection bias.

Throughout this review we note software commands from MRI and fMRI analysis packages such as SPM (http://www.fil.ion.ucl.ac.uk/spm, [Ashburner, 2012]), FSL (http://fsl.fmrib.ox.ac.uk/fsl, [Jenkinson et al., 2012]), FreeSurfer (https://surfer.nmr.mgh.harvard.edu, [Fischl, 2012]), AFNI/SUMA (https://afni.nimh.nih.gov, [Saad et al., 2004]), BrainVoyager (http://www.brainvoyager.com, [Goebel, 2012]), MIPAV (https://mipav.cit.nih.gov/, [McAuliffe et al., 2001]), and NiPy (http://nipy.org, [Millman & Brett, 2007]) that perform the specific advanced analysis steps discussed. The commands listed are simply illustrative examples of how to carry out the advanced processing and analysis steps discussed in this review. Often the source code is provided with these packages, so users can also see how these algorithms are implemented in practice.

While the focus here is on analysis strategies tailored to UHF-fMRI, it is important to note at the outset that in addition to increased sensitivity there are potential gains in specificity when moving to UHF-fMRI as well. It is well known that due to the more rapid decrease in T₂ relaxation times in blood with field strength compared to brain tissue, the origin of the BOLD fMRI signal shifts from a predominantly intravascular signal to a predominantly extravascular signal [Uğurbil et al., 2000]. Because of the availability of acquisition techniques, such as Hahn spin echo, that are preferentially sensitive to extravascular signal changes around small vessels in the diameter range of capillaries and small venules [Ogawa et al., 1993; Boxerman et al., 1995; Uludağ et al., 2009], there is potential to restrict BOLD measurements to be sensitive only to the smallest vessels of the parenchyma, which presumably are more neuronally specific, and avoid large draining vessels which are known to shift and corrupt spatial patterns of activation [Olman et al., 2007; Polimeni et al., 2010a]. The increased sensitivity can also be traded off for increased specificity by enabling non-BOLD functional contrast such as measures of cerebral blood flow or perfusion with techniques such as Arterial Spin Labeling (ASL) [Pfeuffer et al., 2002a; Golay & Petersen, 2006; Gardener et al., 2009] or measures of cerebral blood volume with techniques such as Vascular Space Occupancy (VASO) [Jin & Kim, 2008; Hua et al., 2013; Huber et al., 2014b]. Therefore, UHF can provide fMRI with improved specificity as well as sensitivity, and this is another motivating factor for pushing to higher field strengths [see Uludağ et al., this issue, for a full discussion of the specificity gains at UHF]. In general, however, these differences in the specificity of the fMRI signals that can be achieved through advanced acquisition strategies do not fundamentally change the analysis strategies—although the increased specificity may change the interpretation of those data.

2. BUILDING AN ANATOMICAL REFERENCE

All fMRI analyses require an anatomical reference to help interpret the data by identifying which brain region is responding to the stimulus or task, or to help guide the analyses. In some cases, the anatomical reference is also required to fully visualize and characterize the spatial pattern of activation, such as the cortical surface models used in studies investigating topographic or columnar maps. As voxel sizes decrease, activation can be localized to smaller regions of the brain, and finer-scale maps can be visualized. Many different aspects of UHF-fMRI analyses utilize anatomical references, however there are specific challenges to acquiring suitable anatomical reference data at UHF, each of which is discussed in detail below.

Anatomical data acquisition considerations at UHF

Generating accurate surface models from anatomical data acquired at UHF can be challenging due to image artifacts that are more prevalent at higher field strengths. Magnetization-prepared T₁-weighted pulse sequences such as those derived from MPRAGE [Mugler & Brookeman, 1990; van der Kouwe et al., 2008; Marques et al., 2010] are commonly used for anatomical imaging because of their strong gray matter/white matter/cerebrospinal fluid (CSF) contrast and their ability to provide high spatial resolution in reasonable imaging time. These sequences rely on a uniform RF transmit field during the magnetization preparation, which is generated using an inversion pulse. This assumption of the uniform RF transmit field is violated at UHF. If the uniformity is compromised, as is often the case, and the preparation pulse fails to invert spins locally, tissue contrast can be severely degraded. The brain regions most severely affected are those around the inferior temporal lobes, which suffer from both B₀ and B₁⁺ inhomogeneity [Collins et al., 2005], and in practice gray matter and white matter can even appear isointense in regions such as the temporal poles and orbitofrontal cortex. This is a major challenge to accurate cortical surface reconstruction, which must be addressed at the time of acquisition. Specialized adiabatic pulse designs (such as the FOCI pulse [Ordidge et al., 1996; Hurley et al., 2010]) can achieve both a resilience to the nonuniform B₀ field and to the nonuniform transmit or B₁⁺ field.

RF transmit nonuniformity can also affect the excitation pulses. In the case of MPRAGE this leads to a spatially varying intensity bias that is smoothly varying, similar to RF receive coil or B₁⁻ field bias. This bias can be corrected during preprocessing prior to anatomical segmentation and surface reconstruction, resulting in more spatially uniform image contrast. Often, due to the more spatially complex bias field seen at UHF, standard bias correction approaches based on fitting low-order spatial trends are not sufficient, while approaches based on joint estimation of bias and tissue segmentation¹ perform well in practice [Uwano et al., 2014; Renvall et al., 2016], although possibly at the cost of spatial noise uniformity. Furthermore, because most UHF scanners (including whole-body scanners) typically use head-only transmit coils that extend only to the shoulders, even non-selective RF pulses do not reach arterial blood in the heart destined for the head. This causes the arterial blood to be near to equilibrium magnetization (similar to flow-related enhancement in time-of-flight angiography) and results in bright blood vessel artifacts in MPRAGE data when using head-only transmit coils. This can cause artifacts in the pial vasculature that can be mistaken for gray matter. Acquisition strategies based on acquiring a second, proton-density volume matched to the MPRAGE can be used to normalize out these vascular artifacts as well as intensity bias [Van de Moortele et al., 2009].

With the additional sensitivity afforded by UHF, there has been a recent trend towards acquiring anatomical data with voxel sizes smaller than 1 mm. It has been noted that the thinnest cortical regions, like primary somatosensory or visual cortices, can exhibit the high myelin content (and thus low gray-white contrast), which can lead to cortical surface reconstruction inaccuracies when using conventional 1 mm isotropic voxels [Glasser & Van Essen, 2011]. Subsequently, sub-millimeter acquisitions including 0.7 mm isotropic at 3 T [Glasser et al., 2013], 0.5 mm isotropic at 7 T [Lüsebrink et al., 2013] and 0.4 mm isotropic at 7 T [Bazin et al., 2014] have been shown to provide improvements in surface reconstruction and cortical thickness estimates. Although, as previously suggested, some regions do benefit from sub-millimeter resolution, in many brain regions conventional 1 mm voxel sizes provide surface reconstructions with equivalent accuracy [Zaretskaya et al., 2015]², and it is likely that these higher resolution anatomical data may provide different benefits for different segmentation algorithms. Higher resolution (down to 0.25 mm isotropic) is possible with longer scans, which require the use of prospective [Tisdall et al., 2013; Lüsebrink et al., 2017] or retrospective [Federau & Gallichan, 2016] motion correction techniques to prevent deleterious motion artifacts.

As a cautionary note, imaging protocols that enable sub-millimeter voxel sizes often result in reduced tissue contrast, inadvertent spatial blurring, low image SNR, and low tissue CNR, which unfortunately can lead to inaccurate segmentation. Now that increased scanner field strength and available software tools allow for sub-millimeter voxels, there can be a wide variety of resolutions and contrasts available, with varying levels of image quality, yet not all will be suitable for accurate segmentation and surface reconstruction. Nevertheless, the possibility of higher-resolution anatomical data can benefit cerebral cortical reconstruction, enable reconstruction of the cerebellar cortical surface, and enable better delineation of small subcortical structures as well. As UHF-fMRI continues to push to smaller and smaller sub-millimeter voxel sizes, these newly-available high-resolution anatomical reference data with similar voxel sizes can be used to better delineate anatomical borders and quantify partial volume effects to help analyze and interpret the fMRI data. However, successfully incorporating these high-resolution anatomical references into the high-resolution fMRI analysis requires a strict geometric correspondence between the functional and anatomical data.

Distortion-matched functional and anatomical data

One of the most prominent differences between anatomical and functional MRI data is their geometrical inconsistency. While anatomical brain images typically retain relatively well the shape and size of the imaged tissue, EPI data used for fMRI are vulnerable to severe distortions because of the relatively low bandwidth in the phase-encoding direction.

In recent years the quality of EPI has increased dramatically, mostly due to improvements in hardware performance and, notably, due to accelerated parallel imaging techniques. With these improvements it becomes possible to remove the geometric mismatch between functional and anatomical data by simply using the same EPI-based image encoding for both functional and anatomical data, obviating the need for EPI distortion correction—especially if the goal is simply to achieve accurate registration to an anatomical image. Although geometric distortion correction methods are widely available for EPI, inaccuracies in the estimation of the distortion can often yield unsatisfactory results in practice [Hutton et al., 2002; Irfanoglu et al., 2015], making a natively distortion-matched anatomical dataset an attractive alternative.

While geometric distortions still prevent EPI from perfectly matching typical high-resolution anatomical data, it has been recognized that EPI quality is sufficient to provide anatomical reference data, and an approach has been proposed based on utilizing native T₂^*-weighted EPI data for spatial normalization [Huang et al., 2010; Grabner et al., 2014]. However, because the native T₂^* weighted image contrast present in BOLD fMRI data contains many image features within and surrounding the cortical gray matter—such as the intensity variations surrounding large white matter pathways and the regular pattern of signal loss within the large pial vessels on the cortical gray matter surface—these images are currently not well-suited for accurate anatomical segmentation.

T₁-weighted images, such as those provided by MPRAGE, are commonly used in part due to the relatively flat intensity within the gray matter, white matter, and CSF compartments, which makes tissue boundaries less ambiguous and automatic segmentation more robust. However, inversion-recovery EPI acquisitions can also achieve T₁-weighting, using a similar magnetization preparation to that used in MPRAGE, to generate anatomical reference data directly from EPI. Using a pulse sequence similar to previously proposed inversion-recovery EPI schemes [Clare & Jezzard, 2001; de Smit & Hoogduin, 2005], whole-brain 1-mm isotropic T₁-EPI data acquired at 7 T in less than 3 minutes has been shown to provide sufficient quality and tissue discriminability for cortical surface reconstruction as well as automated subcortical parcellation [Renvall et al., 2014b, 2016]. These distortion-matched anatomical data have been shown to provide accurate tissue segmentations and have been used for masking out physiological noise in brainstem fMRI [Beissner et al., 2014a]. Recently this approach has been applied to cortical depth analyses of high-resolution fMRI data [Huber et al., 2016; Kashyap et al., 2016; van der Zwaag et al., 2016]. This approach has also been applied at 9.4 T [Ivanov et al., 2015] and extended to a 3D-EPI acquisition and image reconstruction based on the MP2RAGE method [van der Zwaag et al., 2016]. Moreover, this acquisition technique is compatible with Simultaneous Multi-Slice techniques [Dougherty et al., 2014; Grinstead et al., 2014, 2016; Wu et al., 2015], or slice-order optimization techniques based on MR Fingerprinting principles [Cohen et al., 2016], which can further speed up the acquisition or provide the increased number of slices needed for sub-millimeter acquisitions.

While distortion-matched surface reconstructions can be beneficial for anatomical references in fMRI analysis, it is important to note that, naturally, these surfaces are geometrically distorted and therefore may not be suitable for morphometric analysis, such as cortical thickness measurements. Also, other uses of cortical surfaces, such as surface-based atlasing, may be influenced by the patterns of geometric distortion not present in the conventional anatomical data that formed the atlas. A previous characterization of this effect showed that for cortical regions away from large B₀ inhomogeneity there was good agreement between estimated cortical regions from EPI-derived and MPRAGE-derived surfaces using a standard surface-based atlas, but for distorted regions (mostly near air-tissue interfaces) some disagreement was present [Renvall et al., 2016]. Therefore caution should be exercised when using distortion-matched surfaces to predict locations of cortical areas based on the geometry of the folding pattern. It may be possible, however, to distortion correct the surfaces (using additional information such as a B₀ field map) prior to parcellation (see Geometric distortion correction – image warping and surface-based correction) to improve cortical area prediction accuracy.

Another requirement of this approach is that the T₁-EPI acquisition must have not onlysuitable tissue contrast but also adequate spatial resolution to segment the cerebral cortical gray matter and generate accurate surface reconstructions, thus voxel sizes of 1 mm isotropic [Fischl & Dale, 2000] or smaller [Glasser et al., 2013; Lüsebrink et al., 2013; Zaretskaya et al., 2015] are recommended for adult human brains. For fMRI acquisitions utilizing larger voxels, a suitable anatomical EPI protocol must be developed that is distortion-matched to the functional EPI protocol while having voxel sizes of ≤ 1 mm isotropic. This requires that the anatomical EPI protocol must be designed to have the same slice prescription and phase-encoding axis and direction as the functional EPI protocol, and that the EPI echo spacing and field-of-view must be set to ensure matching distortion. Details on how to achieve a distortion-matched anatomical and functional EPI acquisition with different spatial resolutions are provided in Appendix A.

Anatomical reference for cortical, subcortical, brainstem, and spinal cord structures

While today most applications of UHF-fMRI focus on the cerebral cortex, the small voxel sizes have enabled investigations into smaller structures such as the cerebellar cortex [van der Zwaag et al., 2013; Deistung et al., 2016], the brainstem [see Sclocco et al., this issue] and spinal cord [see Barry et al., this issue]. These studies also require anatomical reference data for interpretation and to guide analysis. Surface reconstructions of the cerebellar cortex are possible with high anatomical resolution [Van Essen, 2002; Sereno et al., 2015], and have been utilized for surface-based analysis of fMRI data [Wang et al., 2014; Diedrichsen & Zotow, 2015]. Similar tools are now being developed to integrate automated anatomical segmentations of the human brainstem [Moher Alsady et al., 2016] or cervical spinal cord [De Leener et al., 2016] into fMRI analyses to help localize tissue boundaries and identify functional sub-regions. Overall, anatomical reference data for studies of cortical or subcortical brain areas are useful not only for identifying activated brain regions and for providing a substrate for group-level analysis, but they also enable powerful, anatomically-informed methods for data preprocessing and statistical analysis. These methods are discussed further below.

Projection and interpolation of fMRI data onto surface meshes

Once the surface reconstructions representing the cerebral cortex have been generated, to proceed with surface-based analysis first the fMRI voxels must be projected onto the vertices of the surface mesh. While this projection can be viewed as simply assigning each voxel’s data to a vertex, it is a form of interpolation that can locally alter the spatial structure of the fMRI data. The most common form of surface projection is nearest-neighbor interpolation, in which the voxel data is assigned to all vertices that it intersects. This approach works reasonably well when the size of the fMRI voxel is greater than the spacing of the vertices in the mesh. Conventionally, cortical surfaces are reconstructed from 1 mm isotropic anatomical data (in which case the typical spacing between vertices is about 0.9 mm for typical reconstructions, for example). However, in UHF-fMRI, submillimeter voxel sizes are becoming more common, and naïve projection onto these meshes can result in some fMRI voxels lying between vertices being “missed” or not projected anywhere onto the mesh. Local distortion of the spatial structure of the fMRI data is possible when the EPI voxel grid and the irregular polyhedral mesh vertices are spatially misaligned, i.e., if some fMRI voxel centroids are far from the closest vertex. Therefore, meshes with sufficiently dense and regular vertex spacing are required to avoid these sampling biases. One brute-force strategy to combat this is to simply upsample the mesh through either approximating or interpolating schemes.³ As higher-resolution anatomical data become more common (see Anatomical data acquisition considerations at UHF), this problem may subside. In any case, it seems advisable to choose the anatomical data resolution needed to accurately resolve the anatomical structures of interest, rather than to choose it based on fMRI data interpolation considerations. The solution of upsampling high-quality meshes from conventional data nicely decouples the decision of choosing the anatomical and functional resolutions.

Other common interpolation schemes are also applicable to surface projection, such as trilinear interpolation, where each vertex is assigned a weighted sum of nearby voxel intensities. Trilinear or other higher-order interpolation schemes avoid some of the shortcomings of nearest-neighbor interpolation listed above. These interpolation approaches, like image interpolation, explicitly introduce spatial smoothness and correlations into the fMRI data as it is projected onto the surface. With small fMRI voxels, it is also possible to increase SNR by projecting onto each surface vertex a weighted sum of voxels across the cortical depths. This is commonly performed by summing all voxels along the straight-line path defined either by the surface normal at each vertex or by the ray connecting corresponding vertices on the white matter and pial surface meshes. Averaging voxels along this straight-line path will cause sampling biases in small curved regions of cortex, where paths from multiple vertices tend to converge, and curvilinear paths that bend with the cortex may be beneficial (see Predicting geometry of columns and layers). Anatomically-informed interpolation has also been proposed, where the weights of the interpolation kernel are adapted to the local geometry of the cortex to avoid noise contamination from extracerebral CSF and signal dilution from subjacent white matter [Grova et al., 2006; Operto et al., 2008].

It is also possible to perform anatomically informed analysis using cortical surface models without projecting the fMRI data onto the surfaces by performing the inverse operation of “projecting the surface vertices into voxels”. By identifying which fMRI voxel contains each vertex of the surface mesh, a volumetric mask corresponding to the anatomical position of a cortical surface can be identified.⁴ While this volumetric mask cannot be used with many of the preprocessing and analysis strategies surveyed here, it can be utilized in cortical depth analyses described in detail below.

3. FMRI DATA PREPROCESSING – SMOOTHING, DISTORTION CORRECTION, AND REGISTRATION

While UHF-fMRI provides the sensitivity boost that enables higher resolution acquisitions, it is still often difficult to achieve the desired resolution with modern UHF systems. High-resolution imaging requires additional image encoding, and many practical constraints exist that preclude arbitrarily small voxels—including hardware limits and safety restrictions as well as sensitivity losses. Submillimeter fMRI acquisition strategies designed to avoid resolution losses—particularly those due to spatial blurring induced by long readout times [Farzaneh et al., 1990]—can be adopted to attain both high nominal and high effective spatial resolution, but often involve some trade-offs, and must compromise temporal resolution or spatial coverage for spatial resolution. In order to truly attain high resolution in practice, care must also be taken in the data analysis so as to not lower the effective resolution by unintentional spatial filtering or smoothing.

Several common fMRI data preprocessing steps that appear in conventional analysis workflows must be revisited when working with high-resolution fMRI data. These steps can introduce unwanted spatial or temporal blurring of the fMRI data, or may lead to systematic errors in interpreting which anatomical regions are responding to a stimulus or task. We consider several standard preprocessing steps used in conventional analysis workflows that can have deleterious effects on high-resolution fMRI data, and survey recent analysis strategies that have been proposed to preserve resolution and increase geometric accuracy.

Image data resampling and interpolation in slice-timing correction and motion correction

Often the first preprocessing step applied to fMRI time-series data is slice-timing correction. In conventional two-dimensional multi-slice EPI, the fMRI data are acquired slice-by-slice over the brain, with each slice acquired at a different time point. Most analysis methods assume that each volume of data is acquired instantaneously, therefore slice-timing correction is commonly applied, and the time-series data from each slice is resampled onto the same time point. This resampling requires interpolation, which can alter the temporal autocorrelation of the time-series data. To perform slice-timing correction, the relative times of each slice must be known, yet the timing can change across EPI protocols (depending on whether the slices are acquired sequentially or in interleaved manner, and can depend on whether the total number of slices is odd- or even-valued), and certainly can change across pulse sequence implementations and vendors. Slice-timing correction is also required for Simultaneous Multi-Slice EPI techniques, which use Multi-Band pulses to acquire multiple slices simultaneously to increase temporal resolution or slice coverage [Feinberg et al., 2010; Moeller et al., 2010; Setsompop et al., 2012; Feinberg & Setsompop, 2013; Barth et al., 2015], however the groups of simultaneously-acquired slices must be known. For slower block-design paradigms slice-timing correction may not be necessary and is often not performed. As temporal resolution increases, and each volume is acquired in a shorter time interval, slice-timing correction becomes less critical. The differences in slice timing can also be accounted for in the statistical analysis by using a slice-dependent time-delay of the fMRI response predictor.

Perhaps the most common and justifiable preprocessing step is motion correction, which seeks to estimate rigid-body head motion and then correct this motion within an fMRI run. Typically, a reference frame is chosen (such as the first frame or the central frame of the time-series data); the alignment between each image frame and the reference frame is calculated, from which the head motion is estimated; then the image data from each frame is rotated and translated accordingly to bring it into register with the reference. This rotation and translation requires the data from each original image frame to be resampled onto the voxel grid of the reference image, and thus the data from each original image frame must be interpolated—each voxel of the corrected image frame is a linear combination of a neighborhood of voxels in the original image frame. Even with high-order interpolation kernels, this linear combination results in resolution loss and introduces additional spatial correlation in the time-series data. While the blurring and resolution loss incurred during motion correction cannot be avoided, the amount of blurring, and its spatial distribution, can at least be estimated to help interpret results. One simple way to estimate this spatial resolution loss or blurring is to apply the resampling and interpolation to a time-series of synthetic white noise, which is independent across voxels and thus spatially and temporally white, then calculate the resulting temporal standard deviation of each voxel. The effective blurring caused by interpolation can be quantified by calculating the width (the full-width at half-maximum, FWHM) of a 3D Gaussian function smoothing kernel, applied to the same noise, that yields the same resulting temporal standard deviation. The results of this calculation used to evaluate the smoothing effects of motion correction are presented in Fig. 1A–D.

Figure 1. Resolution loss by resampling during preprocessing.

The loss of spatial resolution induced by several common preprocessing steps was evaluated by applying the preprocessing to synthetic “time-series” data consisting of spatially and temporally independent Gaussian random noise. The level of smoothing induced by the preprocessing was calculated by explicitly smoothing the same noise time-series data with a range of smoothing kernel widths (parameterized by its FWHM), then finding at what kernel width the temporal standard deviation after explicit smoothing matched the temporal standard deviation after preprocessing. (A–B) Effects of motion correction, using synthetic motion traces where the magnitude of motion was scaled to typical ranges seen in healthy volunteers. (A) Resolution loss as a function of translational motion, where the displacement corresponds to moving from one corner of a cubical voxel to the opposite corner. Resolution loss peaks at a translation of 1/2 of the voxel width. (B) Resolution loss for an example through-plane rotation (head nodding) and various in-plane rotation (head shaking) for an axial slice prescription. A 1° nod causes a symmetric pattern of resolution loss. (Outline of human brain shown for reference.) In-plane rotation centered on voxel 96 causes a resolution loss pattern that varies more rapidly over space with increasing levels of rotation. (C) Resolution losses from through-plane motion (head nodding) of 2° visualized on original and inflated cortical surface. (D) Resolution losses from in-plane motion (head shaking) of 2° visualized on original and inflated cortical surface. (E–F) Effects of EPI geometric distortion correction, using a standard B₀ field map obtained in a human volunteer at 7T. Image unwarping causes resolution loss that both scales with the voxel size and varies spatially according to local field inhomogeneity, as shown on a sagittal slice at 1 mm resolution in (E), and 2 mm in (F). Note that the spatial frequency of the resolution loss pattern is lower in the 2 mm data. (Note different color scales for 1 mm and 2 mm data.) (G) Effects of gradient nonlinearity distortion correction, using nonlinearity coefficients from a standard 7T gradient coil. The specific pattern of resolution loss through resampling and interpolation varies by gradient coil rather than by subject or by specifics of the imaging protocol. However, the spatial pattern is complex, and subject positioning will affect the pattern of resolution loss within the brain after this correction. (H) The computed transfer function used to convert the temporal standard deviation to the FWHM of the effective spatial smoothing; this characterizes the effects of image resampling on a white-noise input dataset.

Because there are potential interactions between slice-timing correction and motion correction [Bannister et al., 2007], and both correction steps require interpolating the time-series fMRI data, joint correction of slice-timing differences and head motion⁵ has been proposed [Roche, 2011]. This approach not only reduces the amount of interpolation but can also improve motion correction accuracy by informing the motion estimation algorithm of the times at which each slice is acquired.

Registration between functional and anatomical data

Before the anatomical reference can be used to analyze and interpret the functional data, a registration is required to align the two volumes. Registration techniques are not fundamentally different with UHF-fMRI, but there are several considerations, including what registration to use for high-resolution data, how to register partial-brain data, and how to register in cases where residual geometric distortion may be present in the EPI data.

For high-resolution fMRI data intended for surface-based analysis, the Boundary-Based Registration (BBR) approach has distinct advantages. BBR seeks to determine the registration between the functional and anatomical data that aligns the cortical surface reconstruction extracted from the high-quality anatomical data with the boundary between gray and white matter within the fMRI data [Greve & Fischl, 2009]. Thus, BBR seeks a registration that positions the surface reconstruction (derived from the anatomical data) in the functional volume such that the difference in image intensity across the surface is maximized. It is therefore driven by matching a two-dimensional feature, the cortical boundary, between anatomical and functional data. Because it explicitly seeks to align the cortical surface reconstruction to the cortical boundary in the functional data, it is ideally suited for cortical surface-based fMRI analyses where the accuracy of the positioning of the surface model relative to the fMRI data is critical.⁶

Intuitively, BBR can achieve a more accurate registration of the cortical surface reconstruction to the gray-white interface by relaxing the constraint used in conventional registrations, which seek to align the entirety of the 3D image volumes. Constraints can be further lifted by specifying that the registration be driven by a smaller anatomical region of interest, providing a means to perform restricted registration. This can be helpful in cases where some residual geometric distortion remains in the functional data. One can first calculate an initial, global registration based on the full anatomy, then refine this registration by specifying a smaller anatomical region.⁷ This progressive restricted registration initializes each smaller-region stage by the results of the previous larger-region stage, and helps to avoid local minima in the optimization. Similarly, one can drive the restricted registration based on those anatomical regions that are the most likely to exhibit the best geometric accuracy in the EPI data, essentially by including only those regions far from the known susceptibility regions such as air-tissue interfaces.⁸ These restricted registration approaches are also compatible with conventional volume-based registration.

An additional important feature of BBR is that it can accurately align functional acquisitions with limited partial-brain coverage [Greve & Fischl, 2009]; many conventional registration methods were designed assuming fMRI acquisitions with whole-brain coverage, and can fail when confronted with fMRI volumes that cover a small percentage of the brain. Because of the longer image encoding times for high-resolution fMRI acquisitions, to avoid long repetition times, low temporal resolution, and long imaging times that foster subject motion, these acquisitions often rely on partial-brain coverage. Furthermore, advanced high-resolution acquisition techniques that seek to reduce readouts to decrease geometric distortion, such as “zoomed” imaging [Setsompop et al., 2016]—through outer-volume suppression [Pfeuffer et al., 2002b; Heidemann et al., 2012], inner-volume imaging [Feinberg et al., 1985, 2008], or localized RF coil arrays [Petridou et al., 2013; Farivar et al., 2016; Keil et al., 2017]—are increasingly utilized for UHF-fMRI and also result in smaller imaging fields-of-view and partial-brain coverage. Therefore, registration techniques that are compatible with partial-brain coverage, such as BBR, are particularly helpful for UHF-fMRI. Then, if the fMRI data contain sufficient tissue contrast and SNR, it is possible to perform fMRI motion correction using BBR by aligning each frame in the time series to the anatomical reference.

For fMRI data where the contrast between gray matter and white matter is low, e.g., acquisitions exploiting spin-echo contrast such as 3D-GRASE [Oshio & Feinberg, 1991; Feinberg et al., 2008; Kemper et al., 2015], standard BBR based on the gray-white interface will fail. In these cases, one can either acquire auxiliary data with different acquisition parameters to increase gray-white anatomical contrast (and matching geometric distortions) to aid the registration, or use BBR with the pial surface reconstruction targeting the gray-CSF boundary. Note that BBR can be initialized with an approximate registration between the functional and anatomical data to converge to a solution more quickly. For registering same-session functional and structural data an initial registration step is often not required if there is little head movement between these scans, and the scanner coordinates can be used to provide an initial registration.

Geometric distortion correction – image warping and surface-based correction

Because of the increased magnetic field strength, susceptibility gradients in the head—particularly those caused by air–tissue interfaces such as those found in the frontal sinuses, oral cavity, and ear canals—result in increased field offsets and therefore pronounced distortion in EPI at UHF compared to conventional field strengths. While acquisition strategies exist to partially mitigate these geometric distortions [Setsompop et al., 2016], several millimeters of distortion is still commonplace. For high-resolution UHF-fMRI studies, this distortion is unacceptable and some correction is required.

The techniques for post-hoc distortion correction at UHF-fMRI are not in principle different from those used at conventional field strengths. These techniques fall into three categories: those based on direct measurements of the B₀ field offset [Jezzard & Balaban, 1995; Reber et al., 1998; Chen & Wyrwicz, 1999; Hutton et al., 2002], those based on measuring the impact of the distortion on the EPI data such as the PSF or PLACE techniques [Zaitsev et al., 2004; Xiang & Ye, 2007], and those driven by image registration that calculate the distortion directly from the EPI data such as the blip-up/blip-down methods [Chang & Fitzpatrick, 1992; Andersson et al., 2003; Holland et al., 2010]. Each of these methods calculates the distortion, and then removes it from the EPI data through unwarping. This unwarping of the image data involves resampling of the shifted image data onto the (undistorted) voxel grid and therefore requires interpolation, causing spatially periodic resolution loss and spatial correlations in the data. An example of the resolution loss is shown in Fig. 1E for a 1 mm isotropic EPI acquisition at 7T, quantified by the FWHM of the effective smoothing of the data induced by the interpolation. (A similar demonstration was presented by Renvall et al. in Fig. S5 [Renvall et al., 2016].) This spatial pattern of blurring in a way resembles the B₀ field distribution itself—the spatial periodicity of the pattern is clearly more rapid around air–tissue interfaces such as the frontal sinuses and ear canals. The reason for this pattern is that it reflects the amount of voxel shifting performed in the unwarping relative to the voxel grid—if a voxel is shifted by, say, exactly the distance of 3 voxel-lengths, during resampling back onto the grid no interpolation is necessary, but if a voxel is shifted by the distance of 3.1 voxel-lengths resampling will require some interpolation, and if a voxel is shifted by the distance of 3.5 voxel-lengths, it will be positioned exactly halfway between two grid points and will experience the maximum level of interpolation. This implies that the resolution loss due to interpolation is a function not only of the unwarping but also of the spacing of the voxel grid: a displacement of 5 mm may cause local resolution loss for a 2 mm voxel grid but not for a 1 mm voxel grid. This can be seen in Fig. 1F, where the same unwarping used in Fig. 1E is applied to a 2 mm isotropic EPI acquisition at 7T.

Another form of geometric distortion that is prominent in high-performance gradient coils is gradient nonlinearity distortion arising from deviations of the induced gradient field used for image encoding from a linear function of space [Schmitt, 1985; Langlois et al., 1999]. This causes geometric distortion if these nonlinearities are not accounted for in the image reconstruction. Fortunately these distortions are smoothly varying in space, and in general do not contain singularities and therefore do not induce voxel “pile-up” artifacts that remain an issue for distortion caused by B₀ inhomogeneity. These distortions are not subject dependent but are based on the gradient coil windings, therefore they normally do not change during the life of the gradient coil. Typically the coefficients of a spherical harmonic fit of the gradient nonlinearities are provided by the manufacturer and this distortion correction is built-in to the online image reconstruction, but it is possible to calculate these distortion fields with information from the vendor in order to apply them offline [Wald et al., 2001; Jovicich et al., 2006; Glasser et al., 2013]. Unwarping image data to remove this distortion also results in localized, systematic spatial resolution loss, as shown in Fig. 1G.

It is possible to avoid the spatial resolution losses associated with image resampling and interpolation by performing surface-based distortion correction, where the surface mesh is deformed instead of the image. In the case of correcting EPI data in order to geometrically match the anatomical reference, instead of unwarping the EPI one can apply the EPI distortion to the surface mesh so that the functional and anatomical data are in geometric alignment. Then the fMRI data can be projected onto the surface mesh for further analysis. In this scheme, the vertices of the surface mesh are displaced by the distortion field (i.e. their coordinates are transformed), which does not require data resampling. This warping must not cause any mesh self-intersection, but, for the smooth deformation fields encountered in MRI, self-intersections rarely occur. An example of a deformation field applied to a cortical surface reconstruction⁹ is shown in Fig. 2. This approach highlights how the voxel grid is not a flexible representation of sampled image data. A surface mesh is a less efficient data structure, in that the spatial coordinates of each mesh vertex must be stored, but this provides the flexibility to update vertex positions without requiring additional data resampling.

Figure 2. Example of surface-based distortion correction applied to EPI.

(A) A sagittal reformat of natively axial 1.1 mm isotropic EPI data acquired at 7T. These data were acquired with a IR-EPI acquisition to generate quantitative T₁ maps and T₂^*-weighted images, and cortical surfaces were reconstructed from synthesized T₁-weighted images [Renvall et al., 2016]. A zoom-out of the synthesized T₁-weighted image is shown in inset. The yellow contours represent the intersection of the image plane with the cortical surface reconstructions of the inner and outer boundaries of gray matter. (B) The same EPI frame, overlaid with corrected surface reconstructions (shown in red), which were warped based on the EPI geometric distortions measured from a standard B₀ field map. Note a large displacement along the phase encoding direction (A→P) in some places. The original uncorrected surfaces are shown in yellow for reference. (C) The same EPI frame after geometric distortion correction. The corrected surface reconstructions now exactly match the tissue boundaries seen in the corrected EPI data. Comparing the image data and surfaces in (A) with the image data and surfaces in (C), the warping applied as part of the distortion correction is applied equally to the image data and to the surfaces.

There are, however, several caveats to this surface-based approach to distortion correction. The first is that head motion within or between experimental session often causes the anatomical data to not be in register with the functional data, so when performing this surface-based distortion correction it is advisable to first unwarp a copy of EPI data using conventional methods, compute the registration between the functional and anatomical data, then apply the transformation calculated by the registration algorithm to the anatomical data before applying the distortion fields. So, for example, to apply both B₀ distortion correction and gradient nonlinearity distortion correction to surfaces acquired in a different experimental session from the functional data, first the gradient nonlinearity correction should be applied to the anatomical data based on the head position during the anatomical session, then the gradient nonlinearity correction and B₀ distortion correction should both be applied to a copy of the EPI data. Then, the registration can be computed between the two geometrically-accurate volumes. Finally, the B₀ distortion and the gradient nonlinearity distortion corresponding to the position of the head in the functional session should be applied to the surfaces reconstructed from the anatomical data.

Although surface-based distortion correction can be used to improve the geometric accuracy of the fMRI data while minimizing the effects of interpolation, the distortion also causes a spatially varying voxel size—voxels will enclose larger or smaller volumes of tissue depending on the local distortion in the image. Local distortions could cause nonuniform sampling of the tissue and potential sampling biases. In extreme cases, singularities can arise where the distortion is strong enough to cause voxel “pile-up” effects and irretrievable loss of information. (Vulnerability to pile-up artifacts can be reduced by judiciously choosing the phase-encoding direction and polarity at the time of the data acquisition.) While artifacts due to these singularities cannot be fully corrected, it is possible to at least incorporate knowledge of the distortion—in the form of a map of the deformation field and the Jacobian of the mapping (which characterizes the expansion or compression of the tissue due to the distortion)—to better interpret the data. More sophisticated techniques for assessing distortion and regional resolution loss, such as point-spread function mapping [Zeng & Constable, 2002; Zaitsev et al., 2004; Chung et al., 2011], can provide additional information to assist with data interpretation. Regions where distortion is too severe should be discarded, and, if voxels are discarded from regions of interest, alternative data acquisition strategies to reduce distortions should be considered. In summary, whether or not distortion correction is applied, it is important to know how much distortion is present in the data and to consider the impacts of the distortion when interpreting the data.

As discussed above in Distortion-matched functional and anatomical data, in practice the estimates of the geometric distortion, either from B₀ field map techniques or image-based techniques, can often yield unsatisfactory corrections [Hutton et al., 2002; Irfanoglu et al., 2015], and natively distortion-matched anatomical data—from which surface reconstructions can be generated that are naturally aligned with the functional data—have many advantages. Also, the surface deformation may cause a spatially varying vertex density that is related to the distortion field and therefore could create a sampling bias when projecting the fMRI data (e.g., in places with strong distortion, vertices could bunch and more finely sample the fMRI data). This can be addressed by refining the surface mesh to have uniformly-spaced vertices after the deformation is applied. Another caveat shared by both the surface-based distortion correction and the distortion-matched anatomical reference data approaches is that the fMRI data projected onto deformed surfaces will not be truly geometrically accurate, in that it will not reflect the true anatomical geometry of the brain. This may influence the interpretation of the activation patterns, such as metric characterizations of topographic maps or surface-area measurements of activated cortex. However, once the fMRI data has been projected onto the surface the surface vertices can be reset to their original, anatomically accurate positions. Overall, the added flexibility provided by surface-based unwarping can be a useful approach to achieving geometric accuracy while avoiding harmful losses in spatial resolution caused by image interpolation.

Several methods have been recently proposed that perform multiple preprocessing steps simultaneously, leading to fewer applications of data interpolation and therefore reduced losses of resolution. The joint correction of slice-timing differences and head motion [Roche, 2011] mentioned above is one such example. Similar methods have been proposed to simultaneously correct for geometric distortion and head motion in EPI data [Ernst et al., 1999; Andersson & Sotiropoulos, 2016] that can address interactions between the position of the head (and its effect on the susceptibility gradients along the phase-encoded direction) and distortion.

As a general rule, the fMRI data should be resampled as few times as possible—ideally only once—to avoid multiple interpolations [Glasser et al., 2013]. Ideally the data would never require interpolation, however in practice some level of resampling (e.g., for motion correction) may be unavoidable. One “best practice” for high-resolution fMRI data is to concatenate or mathematically compose all transformations of the fMRI data, such as motion correction, functional-anatomical registration and various geometric unwarping steps, to apply one transformation to the data and thus interpolate once.¹⁰ This concatenation of transformations can of course be carried out using voxel-based or surface-based analysis approaches to limit the effects of interpolation. If the analysis calls for explicit spatial smoothing of the data, additional efforts to compose all transformations may be unnecessary.

Conventional and anatomically-informed smoothing

In addition to implicit spatial smoothing induced through data resampling and interpolation, often explicit spatial smoothing is employed as a preprocessing step. Smoothing data can help reduce noise through averaging, which can help improve SNR and thus detection sensitivity, and remove anatomical variability across subjects prior to spatial normalization. Perhaps more importantly, it helps to impose smoothness in the measured activation. Smoothness is often a valid assumption about the true fMRI activation patterns, and so spatial low-pass filtering can also help to remove spurious activations or false positives found during the analysis. This is the key assumption underlying many multiple comparisons correction techniques such as those based on Random Field Theory and cluster-size correction [Friston et al., 1994; Worsley et al., 1996b], further described below. Unfortunately, the level of spatial smoothness in the true fMRI activation is often unknown, and oversmoothing or undersmoothing the data can bias the results. Indeed, the matched filter theorem from signal processing states, perhaps unhelpfully, that the ideal filter size is that which is matched to the true extent of the activation [Turin, 1960; Worsley et al., 1996a], which of course is typically unknown prior to the fMRI analysis; however there are techniques designed to identify appropriate levels of smoothing to apply to functional activation maps [Worsley et al., 1996a].

While spatial smoothing can be beneficial for enhancing SNR of the data, it can introduce serious spatial artifacts as well. Conventional smoothing applies a convolutional kernel, usually a 3D Gaussian function, over space, which not only reduces noise but blurs the spatial structure of the activation maps. In many locations in the brain, this blurring can cause signal contamination across tissue boundaries, and especially around the folds of the cerebral cortex. Smoothed activation can erroneously bridge opposite banks of a sulcus, where voxels may be nearby in terms of 3D Euclidean distance but far apart in terms of geodesic distance along the cortical sheet. An example of the effects of conventional 3D spatial smoothing is presented in Fig. 3, where activation originally well-confined to the cerebral cortex is displaced across folds and even gives the incorrect appearance of activation within the subjacent white matter [Stelzer et al., 2014]. Smoothing can therefore dramatically affect the interpretation of the activation maps and can bias the activation away from the true site of neuronal activity. In this sense, smoothing can reduce errors due to noise variance but then introduces errors in the form of spatial bias—an example of a classic bias–variance trade-off [Hastie et al., 2009].

Figure 3. Example of the effects of spatial smoothing on the pattern of fMRI activation, demonstrated with high-resolution (0.65 mm isotropic) BOLD fMRI data acquired at 7T.

ctivation is seen within the visual cortex in response to a standard flashing checkerboard visual stimulation. With no smoothing, the activation map is well localized to the cortical ribbon, but with increasing levels of smoothing activation crosses tissue boundaries, spreads across neighboring sulci and gyri, and strong activation appears within the white matter where no neuronal activation is expected. This demonstrates how smoothing can cause severe localization errors and false positive activation within a large number of voxels. (Reproduced from Stelzer et al. [2014], with permission.)

Anatomically-informed smoothing strategies help to reduce noise and impose smoothness priors in the data with reduced signal contamination across tissues and thus fewer artifacts and reduced spatial bias. In particular, surface-based smoothing, which constrains the smoothing by performing 2D spatial filtering of fMRI tangentially along the surface mesh, therefore only smooths fMRI data that are nearby with respect to the geodesic distance along the cortical sheet [Fischl et al., 1999]. This surface-based smoothing approach was proposed several years ago in the context of fMRI analysis and was demonstrated to provide better functional activation localization than volume-based smoothing [Kiebel et al., 2000; Andrade et al., 2001]. Simulations using synthetic BOLD activations and spatially uncorrelated noise demonstrated how both sensitivity and spatial accuracy of fMRI detection could be improved when using surface-based smoothing over volumetric smoothing [Jo et al., 2007], and that in BOLD data acquired at ~2 mm isotropic resolution the locus of activation was shifted far more by volumetric smoothing than by surface-based smoothing [Jo et al., 2008].

Surface-based smoothing is typically accomplished by first projecting fMRI data onto the surface vertices, as described above, then iteratively and uniformly averaging the projected values between neighboring vertices. This iterative neighborhood averaging¹¹ achieves a smoothing effect similar to convolution with a Gaussian function [Andrade et al., 2001; Chung et al., 2005], although it is possible to define other smoothing functions [Kiebel et al., 2000]. Because the polyhedral surface mesh used for representing cortical surfaces is in general not a regular lattice of vertices but rather comprises an irregular graph, smoothing data along the surface with a shift-invariant convolution kernel is not straightforward. Sophisticated edge-preserving or nonlinear surface smoothing techniques, based on filtering kernels whose weights are determined from the data itself, can suppress spurious activation peaks while maintaining the spatial structure within larger regions of activation [Taubin, 1995; Taubin et al., 1996; Grady & Polimeni, 2010]. Typical implementations of surface smoothing assume scalar-valued, real-valued data; therefore, when vector-valued or complex-valued data—such as responses to phased-encoded stimuli used for topographic mapping [Bandettini et al., 1993; Engel et al., 1994; Sereno et al., 1995; DeYoe et al., 1996]—are to be smoothed along the surface, the individual components (i.e., the real part and the imaginary part of the complex-valued data) must be smoothed separately. Similarly, when smoothing phase-valued data it must be first converted to unit-magnitude complex-valued data then decomposed into real and imaginary components to preserve the modulo 2π equivalence.

Given the advantages of surface-based smoothing approaches summarized above, the question arises: Why are these approaches not used more routinely? One simple answer is that they require surface models that are geometrically accurate, and necessitate interpolation of the fMRI data onto these models. For UHF-fMRI applications, where voxel sizes tend to be much smaller than the cortical thickness, treating the cortical gray matter as a topological 2D surface in order to smooth the fMRI data may seem inappropriate. However, with additional prior information, this anatomically-informed smoothing can be adapted to small-voxel acquisitions by extending the approach to intracortical smoothing strategies. In cases where the voxel size is smaller than the cortical thickness, one can utilize an anatomically-constrained 3D smoothing based on a smoothing kernel contained within the cortical gray matter ribbon—using, for example, locally prolate or oblate kernels, i.e., “steerable filters” whose axes tilt with and track the folds, such that the kernel is parallel to the local coordinate frame of the ribbon and travels within the cortex; it has been demonstrated that this anatomically-constrained 3D cortical smoothing can increase the time-series SNR of a small-voxel acquisition to that of a conventional-voxel acquisition with only a moderate amount of smoothing [Błażejewska et al., 2016]. By allowing the smoothing kernel to extend in three dimensions, but constraining the kernel to remain within gray matter and thereby reduce noise contamination from partial volume effects with CSF, this approach can result in less noise than conventional-voxel acquisitions [Błażejewska et al., 2016].

With additional prior information regarding the spatial structure of the expected activation pattern, the concept of intracortical anatomically-informed sampling can be further extended for small-voxel acquisitions. For studies investigating systems with a known columnar architecture, where there is a strong prior that functional activation should be similar in the direction normal to the cortical gray matter, one can perform a 1D radial smoothing across the cortical depths. Similarly for studies investigating known laminar architecture, where there is a strong prior that functional activation should be similar in the direction parallel to the cortical gray matter, one can perform a 2D tangential smoothing along each intermediate intracortical “laminar” surface[Sereno et al., 2013; Polimeni et al., 2015; Błażejewska et al., 2016]. These intracortical smoothing approaches require accurate knowledge of the geometry of the columns and layers within the cortex and how they shift and bend with the folding pattern (see Predicting Geometry of Columns and Layers below). Small-voxel acquisitions therefore provide many options for intracortical, anatomically-constrained smoothing that simultaneously enforce strict sampling of fMRI voxels only from the cortical gray matter, while avoiding physiological noise contamination from extracerebral CSF and spatial errors introduced by smoothing across tissue boundaries.

4. FMRI STATISTICAL ANALYSES FOR HIGH-RESOLUTION DATA: INTRACORTICAL AND SURFACE-BASED APPROACHES

The basic fMRI statistical analysis applied to UHF-fMRI data is identical to the standard analysis applied at conventional field strengths, however, as discussed above, the higher resolution afforded by increased field strengths enables new analysis approaches to examine activation patterns at smaller scales and with greater spatial accuracy. As voxel sizes decrease to dimensions far below the thickness of the cortex, more precise localization of the activation becomes possible.

Cortical surface-based analyses of fMRI data have long been used to visualize and characterize two-dimensional spatial patterns of activation on the cortical surface [Sereno et al., 1995; DeYoe et al., 1996; Teo et al., 1997]. The surface provides a useful means to establish a 2D coordinate system that respects the intrinsic geometry of the cortical ribbon. With this 2D surface coordinate system, it is possible to measure geometric features of spatial patterns of activation and organization such as topographic maps. It is also possible to use this 2D coordinate system to characterize spatial gradients of the activation and measure how rapidly activation drops-off along the cortex [Spiridon et al., 2006].

A new analysis paradigm in human functional neuroimaging that is enabled by small-voxel fMRI acquisitions is cortical depth-dependent or laminar fMRI [Gati & Menon, 2002; Ress et al., 2007; Koopmans et al., 2010; Polimeni et al., 2010a; Olman et al., 2012; De Martino et al., 2013b; Huber et al., 2014a, 2015; Muckli et al., 2015; Fracasso et al., 2016], which can also benefit from surface-based analysis approaches [Polimeni et al., 2010a; De Martino et al., 2013b]. Because most laminar fMRI studies are conducted at UHF, we will give particular consideration to laminar analysis and to the related cortical-depth analysis approach.

Cortical depth analyses

As the size of fMRI voxels becomes small compared to the thickness of the cortical ribbon, it becomes possible to examine fMRI activation as a function of cortical depth. This not only allows for mapping activation within the cortex to potentially examine laminar and columnar patterns of activation (discussed further below), but can be also used to look for effects that vary systematically as a function of cortical depth. Here we define “cortical depth” as a measure of an fMRI voxel’s relative depth position within the cortex, typically as a percentage of the local cortical thickness; this is distinct from “laminar depth” which accounts for the shifting of layer positions along the folding pattern and is discussed in detail in the following sections.

There is a distinct asymmetry in the size and distribution of blood vessels along the vascular hierarchy, and a fixed relationship between the vasculature and the cortical anatomy that can be exploited to understand the influence of the vasculature on the fMRI signals. The largest blood vessels lie along the pial surface, while the smallest micro-vessels and capillaries are deep within the parenchyma. This arrangement of the vessels causes the BOLD fMRI signals near the pial surface to be less spatially specific. Also, because the extravascular BOLD signal extends beyond the vessel wall and falls off rapidly with distance, and because voxels sampling progressively further from these surface vessels will exhibit diminishing partial volume effects, the pial vasculature exerts influence in the upper layers of the cortex, especially for acquisitions sensitive to large-vessel effects like conventional gradient-echo BOLD. Therefore, cortical depth analyses provide a convenient way to assess the influence of the large pial draining vessels on fMRI data, especially for investigations of columnar features of the cortex like the well-known topographic maps in sensory cortices. This analysis approach has been used to demonstrate the influence of large pial vasculature on spatial resolution within V1 using a retinotopic stimulation paradigm [Polimeni et al., 2010a] and the ability of gradient-echo techniques to achieve sufficiently high spatial specificity to detect an extrastriate columnar system—the V2 stripe system—provided that voxels sampling from the cortical surface are omitted [Nasr et al., 2016]. This approach has also been used to demonstrate that the across-subject variability of tonotopic maps in human primary auditory cortex, and the agreement between individual-subject maps and a recent model of the topographic layout, are both improved by removing gradient-echo BOLD voxels sampling the pial surface and considering only those voxels sampled away from these large draining vessels [Ahveninen et al., 2016]. Recent studies have similarly exploited the high-resolution afforded by UHF-fMRI to examine depth-dependent activation profiles and fine-scale functional organization within the hippocampus [Maass et al., 2014] and other subcortical structures [Loureiro et al., 2017].

One could conclude from these cortical studies that small-voxel fMRI data should always sample far away from the pial vasculature (i.e., from the deepest layers in the cortex, nearest to the white matter) to achieve high spatial specificity, but it is important to note that the signals measured from the pial vasculature may be spatially displaced but still represent the aggregate neuronal responses from a cortical domain and thus are meaningful. Furthermore, because the signal changes have been observed to be largest at the pial surface, one can achieve lower specificity but higher sensitivity when sampling in the shallow layers of the cortex. Therefore depth sampling provides a convenient tool for trading off between specificity and sensitivity, with different studies prioritizing one over the other.

There are two categories of approaches taken in cortical depth analysis to define the relative cortical depth of a given voxel, given as the percent depth normalized by the local cortical thickness. The voxel-based approaches calculate the distance between each voxel’s centroid and the nearest locations on the interior boundary surface of the gray matter ribbon (i.e., the interface between the cortical gray and subjacent white matter, a.k.a., the “white matter surface”) and on the exterior boundary surface (i.e., the interface between the cortical gray matter and the extracerebral CSF, a.k.a. the “pial surface”). This distance can either be a straight-line distance calculated as the Euclidean distance in three-dimensions, or a curved-path distance where the paths are defined from a local orthogonal coordinate system that bends with the cortical folding (calculated, e.g., using the solution to the Laplace equation [Jones et al., 2000; Schmitt & Böhme, 2002; Leprince et al., 2015], described below). The percent cortical depth can then be defined as the distance from the voxel to the white matter surface normalized by the sum of the distance to the white matter surface and the distance to the pial surface which approximates the local cortical thickness. This approach has been used extensively in cortical depth and laminar fMRI studies [Ress et al., 2007; Polimeni et al., 2015; Fracasso et al., 2016]. The surface-based approaches start by generating a family of intermediate surface reconstructions throughout the cortex, e.g., 9 intermediate surfaces spaced across the cortical thickness, plus the 2 boundary surfaces, yielding a total of 11 surfaces spanning the cortex. Then, voxels are projected or interpolated onto each of these surfaces, producing, in the case of the above example, 11 maps of the fMRI data across the cortex. Some implementations of this approach¹² will iteratively propagate one of the boundary surfaces, such as the white surface, through the cortex out to the opposite boundary, periodically saving the intermediate surfaces. Another variant of this approach is to generate an intermediate family of implicit iso-surfaces comprised of a local orthonormal grid coordinate system.¹³

Voxel-based approaches have the advantage that any given voxel is counted only once and is assigned a unique cortical depth, therefore generating an average cortical depth profile over a given region requires simply computing the histogram of the voxel intensities binned by cortical depth, and the bin size and the number of depths sampled can be easily adjusted [Polimeni et al., 2015]. The disadvantage to this approach is that for typical high-resolution fMRI voxel sizes (say, 0.8 mm isotropic) in general it is not possible to generate a cortical depth profile at any one location of the cortex, since at any one location there may only be 2–4 voxels spanning the cortical thickness. Therefore, profiles must be generated by pooling a sufficient number of contiguous voxels.

The surface-based approach has the advantage that it allows the fMRI activation pattern tangential to the cortical surface to be visualized as a function of cortical depth. This approach to sampling the fMRI data across cortical depths mimics the histological processing approach of unfolding and flat-mounting excised cortical tissue, and then tangentially sectioning and staining the tissue [Tootell et al., 1981; Horton & Hedley-Whyte, 1984; Olavarria & Van Sluyters, 1985; Sincich et al., 2003]. The flat-mounting and tangential sectioning technique was employed in classic studies and was instrumental in revealing the tangential spatial organization of columnar systems within the cortex [Tootell et al., 1981, 1982; Horton & Hedley-Whyte, 1984; Livingstone & Hubel, 1984]. It also has the natural advantage that, since the cortical depth can be derived from a family of surfaces with the same mesh or grid topology and a natural vertex correspondence across the family of surfaces, it is straightforward to generate a cortical depth profile at each location along the cortex. This vertex correspondence enables this family of two-dimensional surfaces to represent the layered, three-dimensional structure of the cortex, providing a convenient local coordinate frame that reflects the cortical architecture. Still, for typical high-resolution fMRI voxel sizes there will only be 2–4 voxels spanning the cortical thickness. A disadvantage to this approach is that, depending on voxel sizes and mesh resolution, a given voxel can either be projected onto multiple surfaces within the family, therefore it can be counted more than once in an analysis, or for coarse mesh resolutions some voxels may be omitted. If vertex density varies with curvature, this can induce curvature-dependent sampling biases. Another disadvantage is that, depending on the coarseness of the mesh, if voxel data is projected onto the vertices using nearest-neighbor interpolation there may be some lateral displacement of the voxel data, causing a local shearing effect. While both disadvantages can be addressed by ensuring a sufficiently dense mesh, as described above, this comes at the cost of increased memory requirements and computational burden.

Laminar and columnar fMRI analyses

The family of intracortical surfaces used in cortical-depth analysis described above can also be employed for surface-based laminar and columnar analyses. An important extra step needed to perform laminar analysis is a means to estimate the positions of the layers, and this is considered in detail below. But first, some basic considerations on how to measure functional differences between columns and layers are provided.

A common question regarding laminar analyses is how can one resolve activations from specific layers or even sub-layers (like the stria of Gennari) with voxels that are impressively small (down to 600 μm isotropic) but still not as small as the dimensions of layers, which can be less than 200 μm. It is true that laminar activation cannot yet be resolved, per se, with human fMRI, but given enough voxels sampling across cortical depths it is possible to compare average activations between different layers to assess whether they exhibit any functional difference. With a large enough number of voxels sampling the cortical ribbon, each cortical depth is sampled evenly, as shown in Fig. 4, allowing for a comparison of activation without a sampling bias that favors one cortical depth over another.

Figure 4.

Effects of the ROI size on the uniform sampling of cortical depths. (A) A histogram of the cortical depths sampled by a collection of voxels intersecting a small ROI within the visual cortex. The ROI location is shown in orange on the cortical surface reconstruction (and is indicated with arrows). In this small ROI (~20 mm², or ~40 vertices), the cortical depths are sampled unevenly, with a bias towards the pial surface and the white surface. This clear sampling bias could influence any measurement seeking functional differences between depths. (B) A slightly larger ROI (~310 mm², or ~575 vertices) improves the uniformity of sampling across depths, but a small bias towards the white surface remains. (C) A larger ROI (~2500 mm², or ~4000 vertices) achieves a uniform sampling across depths. While it is unclear how uniformly depths should be sampled to eliminate bias, the effects of ROI size on sampling bias should be taken into account during analysis.

The surface-based tools of cortical depth sampling developed for investigating laminar patterns of fMRI activation can also be employed for characterizing columnar patterns of activation. While there are many columnar features in primary sensory areas well-known from classic studies in animal models, identifying columnar patterns in the human cortex requires establishing, for example, that neighboring voxels in the radial direction have more similar response properties to a particular stimulus or task than neighboring voxels in the tangential direction. Recent studies in the human visual [Zimmermann et al., 2011] and auditory [De Martino et al., 2015] systems have demonstrated a spatial pattern of fMRI responses that appear to reflect columnar organization. A recent study investigating the well-known thick–thin–pale stripe system in V2 [Nasr et al., 2016] also attempted to quantify whether the responses were “columnar” to help argue that the spatial patterns in the data was reflecting this columnar system. In this study the similarity of BOLD responses across depths was quantified by comparing the activation measured in the direction perpendicular to the cortex with activation measured in the direction parallel to the cortex. It was demonstrated that responses measured within columns were more consistent between voxels sampling from the superficial and deep layers than responses measured across columns between voxels sampling only the deep layers (where the spatial pattern of activation was most faithful to the expected pattern of V2 stripes). While this analysis cannot definitively prove that these patterns result from a columnar organization, this was a quantitative test of the similarity of the activation detected across cortical depths within putative columns of the mapped V2 stripe system to see whether the fMRI activation was consistent with a columnar organization. This approach can be extended to map columnar structures without making prior assumptions of the spatial scales or patterns of columnar architecture by comparing spatial gradients of functional activity in the radial and tangential directions, both to identify columnar organization and detect columnar boundaries.

Given the limited biological resolution of fMRI, if similar functional properties were detected across depths at a particular location of cortex, this similarity could reflect either true functional similarity at the neuronal level or the limited spatial specificity of the BOLD response, i.e., the signals measured within small voxels sampling across cortical depths could be intrinsically coupled through the local vasculature. Unfortunately, there is a grid-like regularity of the local vascular anatomy that closely resembles the layout of cortical columns and layers. It is well known that the principal arterioles and venules, which supply and drain the parenchymal capillary bed, are small vessels that are oriented perpendicularly to the cortical surface, and in humans are spaced approximately every 0.75–1.0 mm [Duvernoy et al., 1981], similar to the spatial periodicity of many columnar systems within V1. This conspicuous organization has led to theories regarding the tight functional interrelationship between these “vascular units” and columnar units [Gardner, 2010; Harel et al., 2010], which may or may not hold across brain areas [Blinder et al., 2013; Adams et al., 2014]. Nevertheless, these small intracortical vessels reflect a potential coupling of the hemodynamic signals across depths. Due to their small sizes, it is possible that even techniques with microvascular weighting could still be sensitive to BOLD signal changes within these radial vessels [Uludağ et al., 2009]. These radial vessels would impose a spatial spreading perpendicular to the cortical surface (which implies a spatial asymmetry in the biological point-spread function [Polimeni et al., 2010a]). For this reason, to establish that similar BOLD responses across depths reflect a true similarity of function at the neuronal level would require accounting for the potential artifactual coupling imparted by the spatial spread of the BOLD response. Indeed, given the presumed similarity in neuronal function across the cortical depths at a particular location along the cortical surface, it would be quite challenging to demonstrate definitively the spatial independence of BOLD voxels so close to one another.

This vascular coupling of BOLD signals across depths impacts the ability to detect functional activation within individual cortical layers as well. Because small intracortical venules drain deoxygenated blood from deeper layers up through superficial layers up to the pial vasculature, neuronal activation within the deep layers can trigger BOLD changes across all layers due to this downstream effect. To account for this effect, recent studies have attempted to build explicit models of intracortical fMRI signal changes that accounts for the vascular coupling across layers induced by the radial intracortical vasculature [Markuerkiaga et al., 2016]. Further complicating these models, the regular geometry of the cortical vasculature—including pial vasculature extending tangentially over the cortical surface and principal intracortical venules extending radially across the cortical depths—causes the pial vessels and principal intracortical vessels exert an influence on the BOLD signal that is a function of the angle between the local cortical surface normal and the orientation of the main magnetic field or B₀ [Gagnon et al., 2015]. Because of this, both the signal contamination from large pial vessels and the coupling of the hemodynamic signals across cortical depths will to some extent vary systematically across the cortex, presenting additional challenges for laminar fMRI studies.

Predicting geometry of columns and layers

For the intracortical fMRI analysis of columns and layers described above, it is necessary to know the basic geometry of these architectonic features and how they shift and bend with the folding pattern. It is well-known that the position of the cortical layers varies systematically with the cortical folding pattern—perhaps counterintuitively, the infragranular (lowermost) layers are compressed in sulci and expanded in gyri, and the supragranular (uppermost) layers are compressed in gyri and expanded in sulci. This compression and expansion causes an exaggeration of the curvature of Layer IV within the cortex and causes the depth of Layer IV to change with the curvature of the cortical ribbon [Bok, 1929; Van Essen & Maunsell, 1980; Hilgetag & Barbas, 2006]. As a result, while cortical depth is straightforward to calculate for any given fMRI voxel given a segmentation of the gray matter, estimating the positions of cortical layers is somewhat more challenging. Because of this, fMRI studies investigating functional differences between putative cortical layers must either directly image the anatomical locations of the layers or attempt to infer or predict the locations from the folding pattern.

An early technique for defining cortical depth in a way that respects changes in the geometry of the folding pattern was based on solving the Laplace equation in the cortex. This method uses the interior and exterior borders of the gray matter as boundary conditions, and defined cortical depth as the 2D equipotential surfaces of the solution [Jones et al., 2000]. This technique has the added benefit of providing a means to define 1D contours orthogonal to 2D equipotential surfaces, i.e., the streamlines, which can be used to define laminar profiles across depths or to sample along the columnar direction [Schmitt & Böhme, 2002; De Martino et al., 2013b]. While the solution to the Laplace equation provides a convenient local 3D coordinate system, these solutions do not align well with the locations of the cortical layers [Annese et al., 2004; Waehnert et al., 2012; Leprince et al., 2015].

Another approach to estimate layer positions is to exploit the strong (negative) correlation between the height of Layer IV relative to the white matter boundary and the signed mean curvature (under the convention of an outward-positive surface normal) of the cortical folding pattern [Polimeni et al., 2010b]. The correlation between the height of Layer IV, i.e., the distance between the white matter surface and the interface between supragranular and infragranular cortex, is demonstrated in Fig. 5, where the Layer IV position was detected in 150 μm isotropic ex vivo data covering the occipital lobe of a fixed human brain. The mean curvature of the surface reconstruction was negatively correlated with the absolute Layer IV height with a Pearson correlation coefficient of r = −0.46. This suggests that, with Layer IV acting as an anchor point, cortical layer locations can potentially be predicted in vivo from the easily observable mean curvature of the cortical folding pattern.

Figure 5. Ex vivo modeling to estimate layer positions.

(A) Ex vivo human hemisphere scanned at 7T at 150 μm isotropic resolution, overlaid with cross-section of white matter surface reconstruction from image data acquired in a 1.5T scan session (arrowhead indicating calcarine sulcus). Differential mechanical and imaging distortions between the two sessions result in mismatch between the surface reconstructions and the gray-white tissue boundary. (B) The surface is deformed by matching measured image intensity profile (green) with idealized template (red). Steps in intensity template represent white matter and Layer IV surface positions. (C) Deformed white matter surface. (D) Deformed Layer IV surface. (E) Thresholded mean curvature of the cortical folding pattern. (F) Absolute distance between white matter and Layer IV surfaces overlaid on cortical surface. The distance is highly correlated with the mean curvature pattern. This suggests that the position of Layer IV can potentially be estimated from folding patterns in individual in vivo subjects.

One innovative way to account for the effects of curvature on the estimation of cortical depth profiles is to regress out mean curvature [Sereno et al., 2013]. This is accomplished one depth at a time by assembling the intensities across all vertices for the given cortical depth into a vector, then regressing this against a vector of mean curvature values (either taken from the corresponding depth surface or a fixed reference surface), repeating this procedure for each depth, and then generating the depth profile from the residuals of the fit. This acts to provide depth profiles without the influence of mean curvature, albeit assuming a linear relationship between mean curvature and the influence the variable positions of the anatomical layers have on image intensity.

A more principled approach to defining cortical layer positions is to exploit the observation by Bok that the position of the granular layer (approximately Layer IV) provides an equal volume of cortex in the supragranular and infragranular layers within a cone-shaped region centered at each point of the cortex [Bok, 1929]. This equi-volume principle has been implemented computationally and compared to both the solution to the Laplace equation and to sampling simply by cortical depth (a.k.a. equi-distant sampling) using high-resolution ex vivo brain data (in which the layers could be clearly detected anatomically); the equi-volume sampling was found to provide a better prediction of the layer positions [Waehnert et al., 2014].¹⁴ Recently, this equi-volume principle for estimating laminar depth was merged with the Laplace equation approach used only for estimating curvilinear 1D profiles across depths that track the local columnar arrangement of neurons [Leprince et al., 2015]. The advantages of equi-volume sampling have been demonstrated in high-resolution multi-modal anatomical data [Waehnert et al., 2016] and diffusion imaging data [Kleinnijenhuis et al., 2015].

Like measures of cortical depth, these laminar depth estimates can be computed with voxel-based or surface-based approaches. Voxel-based approaches, using level-sets [Waehnert et al., 2014], implicit surface models [Kleinnijenhuis et al., 2013], or standard partial differential equation framework [Leprince et al., 2015] have been employed, which provide laminar depth estimates with resolutions that match that of the anatomical reference data. In surface-based approaches, surface meshes are positioned within layers and provide a means to generate anatomically-meaningful tangential cross-sections of the folded cortex to visualize patterns of activation as a function of cortical layer.

Both the curvature regression and equi-volume approaches have been shown to remove some of the effects of the shifting positions of the layers across the folding pattern, but neither is perfect. It has been shown that both methods can generate predictions of Layer IV of primary visual cortex that deviate systematically across subjects [Tardif et al., 2013; Hinds et al., 2015]. Nevertheless, these approaches to defining a true “laminar depth” are more accurate for laminar MRI or fMRI studies than sampling by cortical depth. Ideally, anatomical imaging with sufficient spatial resolution can be acquired during the same experimental session as the laminar fMRI data to detect the positions of the layers directly in each subject to avoid any errors associated with predicting layer positions. Inaccuracies in the estimation of laminar position can cause signals from different layers to blur together when pooling voxels to calculate laminar profiles. This can reduce discriminability of functional activation within layers, and this blurring effect is exacerbated with increasing partial volume effects. Methods to reduce partial volume effects are considered below.

Surface-based partial volume correction

Although the voxel sizes in UHF-fMRI have decreased dramatically in recent years, they are still often larger than the anatomical structure of interest, and therefore partial volume effects are common. Partial volume correction techniques have been proposed that can help estimate anatomical or functional data at a sub-voxel level, provided that an accurate measure exists of the composition of each voxel [Choi et al., 1991]. These techniques generally operate by forming a forward model that describes how the observed image intensity in a given voxel is generated from a combination of “true” intensities of each of the constituent tissues weighted by the partial volume fraction of each tissue, and a linear combination is typically assumed (although nonlinear combination models have also been proposed [Duché et al., 2014]). The true intensities are then estimated by selecting a collection of voxels sampling from the same tissue classes, and inverting this model by solving the corresponding overdetermined system of linear equations. For example, to infer the true gray matter, white matter, and CSF intensities from a collection of 2 mm isotropic EPI voxels with various degrees of partial volume effects, given a suitably-sized collection of EPI voxels and an accurate estimate of the percentage of each EPI voxel occupied by gray matter, white matter, and CSF, an estimate of the true intensity of gray matter, white matter and CSF within that group of EPI voxels can be inferred.

Partial volume correction has been applied to anatomical imaging of the cerebral cortex to distinguish between infragranular and supragranular cortical layers from conventional structural data [Shafee et al., 2015]. In the context of UHF-fMRI this partial volume correction has been combined with cortical depth analysis to infer depth profiles of physiological noise contributions [Polimeni et al., 2010c] based on a surface-based approach to defining partial volume of fMRI voxels [Polimeni et al., 2010a].¹⁵ It has also been recently applied to task-driven UHF-fMRI data [van Mourik et al., 2015] to infer fMRI signals generated from specific cortical layers. It is natural to apply partial volume correction to inferring fMRI activation within layers because it is possible to estimate the borders of layers based on the layer position prediction techniques surveyed above. Inferring fMRI signals from individual cortical columns, however, may be more challenging because it is less straightforward to guess the anatomical boundaries of cortical columns than it is to estimate the boundaries of layers!

In the context of applying partial volume correction to infer laminar fMRI signals, this procedure has also been referred to as a “spatial GLM” [Kashyap et al., 2016] due to its similarity to a general linear modeling (GLM) used for detecting fMRI signal changes across the brain. The partial volume for any given tissue corresponds to one design matrix regressor over the collection of voxels and each tissue class of interest is represented by a column in the design matrix, the observations are the image intensities across the collection of voxels, and the solution provides estimates of the β coefficients corresponding to the true intensity for each tissue of interest.

There are important caveats to partial volume correction techniques. First, there are several possible models to employ for the partial volume correction, and in the context of large-voxel Positron Emission Tomography data it has been shown that different models can lead to quite different solutions for the underlying image intensities within cortical gray matter, white matter, and extracerebral CSF [Greve et al., 2016]. Second, partial volume estimates themselves can be inaccurate, and this error can propagate into the true image intensities. When applied to estimating the true fMRI signals from cortical layers, any error in the estimation of the layer position will cause an error in the mixture model and subsequently an error in the solution. However this can potentially be improved by incorporating into the model information regarding the confidence of the partial volume estimation [González Ballester et al., 2002]. Third, the model inversion can become unstable if there is a strong degree of linear dependence between the collection of voxels with regard to their sampling of the underlying tissues. In regions where the cortex is locally flat and the voxels within the collection all have similar partial volume effects, the system of linear equations can become rank deficient, leading to instability in the inversion, which can amplify noise. This noise amplification may vary along the cortex since the conditioning of the system of equations is a function of the local curvature and thickness of the cortex. Fortunately, the conditioning of the system can be evaluated, and can be subsequently improved by increasing the size of the collection of voxels; or the condition number can be used to estimate confidence in the solution. Because the definition of the collection of pooled voxels has a strong influence on the accuracy and stability of the solution, care must be taken to choose a collection size that is large enough for the solution to be stable but small enough to provide an accurate estimate of the local tissue intensities (another bias–variance trade-off). Nevertheless, this approach to partial volume correction of fMRI signals in the context of laminar analysis will likely improve the ability to accurately localize activation to within individual cortical layers.

Sources of signal detection bias in intracortical fMRI

It has been clearly demonstrated in animal models using combined two-photon microscopy of blood vessel diameter changes combined with high-resolution BOLD fMRI [Tian et al., 2010], and in humans with UHF-fMRI [Siero et al., 2011, 2015] that temporal characteristics of the BOLD hemodynamic response function (HRF) change systematically along the vascular hierarchy. As expected, the spatial characteristics vary as well [Polimeni et al., 2010a; Puckett et al., 2016]. Therefore the spatiotemporal HRF is a function of cortical depth. For example, an initial dip in the BOLD HRF was observed in the superficial layers near the pial vasculature but was not observed in deeper layers within the parenchyma, suggesting that this particular feature of the HRF may be attributable to a small temporal mismatch between components of the BOLD response at the cortical surface [Tian et al., 2010; Uludağ, 2010; Siero et al., 2015]. This suggests that GLM-based analyses of laminar fMRI responses may exhibit a systematic bias with depth if the HRF chosen for any given experiment is more similar to the true hemodynamic response of one layer than another.

Biophysical simulations of the BOLD response, as measured with conventional gradient-echo acquisitions, have shown that there is a clear dependency of field strength on the shape of the hemodynamic responses function, with more pronounced transients observed at higher field strengths [Havliíček et al., 2015]. It is possible that the differences of the HRF across cortical depths may be amplified with higher field strengths as well; the opportunities and implications of these field strength dependent effects are discussed elsewhere in this special issue [see Uludağ et al., this issue].

Mis-modeling the shape of the HRF becomes more problematic in fMRI data with faster sampling rates, where is it possible to resolve differences between the expected and observed HRF. Not only do inaccuracies in the HRF cause biases in the detection of activation and decreases in the values of regression coefficients and estimates of percent signal change, but the additional fluctuations in the time-series data residuals after GLM fitting caused by inaccurate HRF models (referred to as “model noise” [Greve et al., 2013]) can influence estimates of noise variance and therefore can alter the GLM statistics as well.

Similarly, it is possible that, with increasing spatial and temporal resolution, additional anatomical differences across the cortex could influence the shape or amplitude of the HRF, causing additional sources of detection bias across layers. It is well known that various differences in anatomical properties such as myelin density, tissue iron density, microvessel/blood iron density, cell density, cell type, and metabolic rate vary systematically across depth [Weber et al., 2008; see also Duyn, this issue], which could cause differences in apparent BOLD amplitudes between putative layers even if the level of neuronal activity is constant across depths. Indeed, a TE-dependent “bump” has been seen in the laminar profile—a local increase in BOLD amplitude was seen for short TE values but vanished for longer TE values [Koopmans et al., 2011]. This may reflect the higher concentration of iron in Layer IV, or perhaps the higher capillary density, or perhaps something else, but it nicely highlights some of the difficulties in interpreting activation profiles when the sensitivity of the measurement varies systematically across depths. These sources of bias may be particularly problematic when estimating functional connectivity across layers from resting-state data, where the subtle fluctuations of the fMRI signal driven by neuronal activity may be small compared to physiological noise fluctuations.

In summary, the shape of the HRF appears to vary with depth, as does the percent signal change (when using conventional gradient-echo-based fMRI) and physiological noise levels. It is possible that advanced acquisition strategies may result in response profiles that vary less with cortical depth [De Martino et al., 2013b], and reduced partial volume effects may help to reduce physiological noise contamination [Heidemann et al., 2012]; however, care must be taken to identify and characterize potential sources for detection bias across depths in order to avoid misinterpretation of laminar fMRI data.

Strategies to circumvent physiological noise

Unfortunately, increased sensitivity to fMRI signal changes of interest, such as those driven by neuronal responses to stimuli or tasks, also leads to increased sensitivity to fMRI signal changes that are not of interest, such as those driven by systemic physiological processes such as respiration, the cardiac cycle, and vasomotion [Krüger et al., 2001; Triantafyllou et al., 2005]. However, because physiological noise fluctuation amplitudes scale with signal level, physiological noise contributions are reduced as voxel sizes shrink. This has motivated the use of small-voxel acquisitions for UHF-fMRI to reduce physiological noise and to take full advantage of the extra sensitivity afforded by UHF [Triantafyllou et al., 2005]. But beyond the ability to suppress the relative contribution of physiological noise, small-voxel acquisitions also help to properly sample the gray matter, both in the cortex and subcortical regions, and reduce the potential for partial volume effects with the surrounding CSF, which is a major source of physiological noise. Because of the high image intensity of the CSF in most fMRI acquisitions, cortical gray matter tissue pulsatility driven by the cardiac cycle can also cause dynamic partial volume effects with the CSF, as local displacement of gray matter causes the CSF contribution within the voxel to change dynamically [Piechnik et al., 2009; Renvall et al., 2014a; Polimeni et al., 2015]; this effect is also reduced with smaller voxel sizes.

Data-driven noise removal techniques, such as those based on Independent Components Analysis or ICA [McKeown et al., 2003; Beckmann & Smith, 2004], are increasingly commonly applied to task-driven and resting-state fMRI data, especially for high-temporal resolution data [Smith et al., 2013]. While these techniques can be directly applied to UHF-fMRI data, because of the stronger physiological noise contributions at higher fields the spatial and temporal patterns of physiological noise must be identified in the UHF-fMRI data for proper removal. It may be more straightforward to separate nuisance components from meaningful components as resolution increases, and anatomically-informed techniques such as surface-based ICA [Formisano et al., 2004] and Masked ICA [Beissner et al., 2014b; Moher Alsady et al., 2016] can help with this separation.

With accurate knowledge of the local tissue boundaries, with small-voxel fMRI, even when high-spatial resolution is not otherwise required, one can simply omit or avoid voxels contaminated by surrounding CSF or major vessels of the extracerebral vasculature, and thereby reduce potential for false positives or structured noise artifacts. This is analogous to the improved physiological noise removal observed when temporal sampling rates sufficiently high to Nyquist sample the noise fluctuations [Smith et al., 2013]. While this strategy sacrifices some image SNR in order to achieve the necessary small voxel volume, the decrease in physiological noise partly compensates the loss. This strategy has been demonstrated in the periaqueductal gray area of the brainstem [Satpute et al., 2013], which is a thin tube of gray matter surrounding the cerebral aqueduct—which is the main passageway connecting the third and fourth ventricles and through which tissue pulsatility rapidly drives CSF, resulting in a major noise source for the surrounding periaqueductal gray. With a high-resolution EPI acquisition (0.75 mm isotropic), strong BOLD activation was detected within and along the periaqueductal gray in response to visual stimuli of graded emotional valence [Satpute et al., 2013]. This strategy has also been demonstrated in the resting-state fMRI analyses of the human brainstem [Beissner et al., 2014b; Beissner, 2015; Sclocco et al., 2016], which is similarly surrounded by pulsatile, noisy CSF and therefore benefits from smaller voxels [Brooks et al., 2013]. In these studies, the noise masking was achieved in the BOLD EPI data with a tissue segmentation provided by a distortion-matched anatomical EPI acquisition [Renvall et al., 2016], as discussed above.

Multiple comparisons correction of high-resolution UHF-fMRI data

Because of the well-known potential for false positive activations in fMRI, correction for multiple comparisons is a standard step in many fMRI statistical analysis pipelines [Nichols, 2012]. There are many approaches to multiple comparisons correction, including Random Field Theory [Friston et al., 1994; Worsley et al., 1996b] and cluster-size thresholding [Forman et al., 1995], both of which provide distributions of the expected extent of “true” activation that can be used to identify spurious activations. These techniques typically require knowledge of the spatial smoothness of the noise in order to identify true activation clusters.

The expected activation extent is a function of the smoothness in the data. Therefore, for fMRI data that have been explicitly smoothed along the cortical surface, as described above (see Conventional and anatomically-informed smoothing), the estimation of the expected activation must also be evaluated on the cortical surface. A framework has been developed for surface-based multiple comparisons correction [Hagler et al., 2006; Saad & Reynolds, 2012] that allows for statistically valid tests to be applied to fMRI data analyzed on the cortical surface.

There are several potential challenges in the application of standard methods for multiple comparisons correction to UHF-fMRI data. With more voxels, the search space will increase, making false positives more likely and causing the problem of multiple comparisons to be more severe. Computationally, the larger number of voxels will trivially affect the processing time for correction methods based on Bonferroni, False-Discovery Rate, and Random Field Theory. However, in computationally intensive methods—such as Monte Carlo based-approaches [Forman et al., 1995] and permutation testing [Nichols & Holmes, 2002]—the processing time is expected to scale linearly. One step common to several of these analysis methods, namely the spatial smoothness or autocorrelation, may become more computationally intense due to smaller voxels necessitating larger numbers of local voxels to estimate smoothness.

Another challenge to these statistical corrections is that some assume that the spatial autocorrelation of fMRI noise is a Gaussian function. For high-resolution studies, explicit spatial smoothing is typically avoided in order to maximize spatial specificity [Stelzer et al., 2014]. Therefore, because this preprocessing step that is commonly employed for conventional fMRI studies—which imparts the required spatial Gaussianity in the noise—is skipped in high-resolution studies, one key assumption of parametric analysis using cluster-wise inferences may not hold in these data. This Gaussian assumption may not be valid in UHF-fMRI data also due to the increased contribution of physiological noise and the spatially structured neuronal fluctuations that are used to infer functional connectivity in resting-state data [Eklund et al., 2016]. Indeed, the ratio of thermal noise to physiological noise in the fMRI data is impacted by spatial and temporal resolution and other acquisition parameters such as parallel imaging acceleration, and can have a substantial impact on the spatial autocorrelation of fMRI noise [Wald & Polimeni, 2016]. Future work will be necessary to incorporate the spatiotemporal structure of the noise into these statistical corrections.

Finally, the spatial smoothness of the fMRI noise is likely to vary substantially across the brain in high-resolution UHF-fMRI data due either to implicit smoothing caused by interpolation (as discussed above), or to the large contribution of spatially-correlated physiological noise; thus, a spatially-varying (or spatially non-stationary) smoothness model may be required [Hayasaka et al., 2004]. Multiple comparisons correction techniques typically estimate smoothness directly from the data (i.e., from the residuals of the time-series GLM fit) and therefore any spatial correlations imparted by the preprocessing or any stage of the analysis will be properly accounted for in these estimates. For laminar fMRI analysis, since there is evidence that specific physiological noise contributions [Polimeni et al., 2015] and spatial autocorrelation [Błażejewska et al., 2016] vary systematically across cortical depths, multiple comparisons corrections applied to intracortical fMRI data should account for this relationship between smoothness and depth. Existing non-stationary approaches may be extended to account for these laminar effects once an appropriate smoothness model is known for intracortical spatial noise correlation.

Multi-variate analysis and decoding approaches

While conventional fMRI analysis approaches operate by applying the GLM to each single voxel independently to detect activation in response to a stimulus or task, it is also possible to extract additional information by multi-voxel or “multi-variate” approaches that jointly analyze groups of voxels. These approaches can be used to better identify the preferred stimulus of a given brain region through techniques such as searchlight analysis [Kriegeskorte et al., 2006] or can be used as input to a pattern analysis or classification algorithm to estimate which stimulus within a set is presented to the subject in an approach sometimes called “brain decoding” or “mind reading” [Norman et al., 2006; Kay et al., 2008; Naselaris et al., 2011; Nishimoto et al., 2011; Tong & Pratte, 2012]. These approaches can be quite successful in discriminating different patterns of activation based on stimulus features encoded at the level of cortical columns [Haynes & Rees, 2005; Kamitani & Tong, 2005]. However, the columnar-level features that are thought to enable successful decoding are often smaller than the voxel sizes [Boynton, 2005; Gardner, 2010; Kriegeskorte et al., 2010a; Shmuel et al., 2010; Chaimow et al., 2011]; hence it is not clear to what extent decoding would benefit from the additional resolution or specificity provided by UHF-fMRI [Kleinschmidt, 2007; Kriegeskorte & Bandettini, 2007; Kamitani & Sawahata, 2010; Op de Beeck, 2010a, 2010b]. It is also possible, however, that large-scale topographic features within cortical areas, which are much larger in scale than cortical columns, contain sufficient information for successful decoding [Freeman et al., 2011], in which case the higher sensitivity of UHF-fMRI may provide benefits that improve decoding accuracy. Multivariate approaches have been applied to cortical depth analysis in a recent UHF-fMRI study, where contextual feedback information was found to peak in superficial depths [Muckli et al., 2015], demonstrating the potential for these techniques to high-resolution data. The application of these multi-variate approaches is considered in greater detail elsewhere in this special issue [see De Martino et al., this issue].

5. GROUP-LEVEL ROI-BASED ANALYSES AND SINGLE-SUBJECT STUDIES

Many fMRI studies seek to compare activation patterns within and across groups of individual subjects. Group fMRI studies have a wide variety of goals, ranging from pooling data across individuals to increase sensitivity in order to detect subtle activation when small effect sizes are expected in fixed-effect analyses, to quantifying how reproducible the pattern of activation is across individuals or groups in order to estimate whether the pattern may be generalizable to populations beyond the studied participants in mixed- or random-effects analyses. Typically, data measured across multiple individuals is compared through spatial normalization, which seeks to align the data from each individual into a common space, such as an atlas, such that in this common space any given voxel represents the same anatomical location across individuals. Spatial normalization is based on warping structural data of each participant into alignment using anatomical and/or functional features detected in each subject, then projecting the functional data into this common space. When the activated regions are large in extent, this spatial normalization works well, because the alignment across individuals is accurate at the spatial scale of individual cortical areas; however for investigations of fine-scale organization commonly performed with UHF-fMRI, it is challenging to derive geometrically accurate alignment at the appropriate sub-areal scale. Indeed, for studies mapping intra-areal topographic maps or columnar organization, the variability of the spatial structure of these organizations may preclude any spatial normalization, making this approach to pooling or comparing activation across individuals inappropriate. Furthermore, for functional or anatomical brain areas that are not well correlated to the macroscopically observable features of the brain—such as the cortical folds [Yeo et al., 2010] or the quantitative tissue parameters sampled onto the surface [Robinson et al., 2014; Tardif et al., 2015] that are used to drive the alignment—spatial normalization may not be an option [Fischl et al., 2008].

Recent studies have shown that fMRI time-courses measured in response to naturalistic stimuli [Sabuncu et al., 2006, 2010]—as well as specific features [Haxby et al., 2011] or networks [Conroy et al., 2013] derived from these responses—can be incorporated into a surface-based registration to improve inter-subject alignment. The performance of this functional activation-driven alignment was evaluated by measuring how well these responses could be used to align a distinct, independent set of functional regions. Features extracted from activation patterns following a battery of functional localizers have also been shown to improve surface-based alignment when combined with geometric features derived from the folding pattern [Frost & Goebel, 2010]. While these functional activation-driven alignment procedures have great potential at UHF due to increased spatial resolution and fCNR, and may help improve across-subject alignment accuracy for group-level analyses, the challenge in applying these methods successfully is to find an appropriate stimulus or task whose activation is independent from the stimulus or task of interest yet can help improve registration.

An alternative strategy to spatial normalization through explicit alignment of data to a common space can be provided by Region-of-Interest (ROI) based analyses. In this approach, an ROI is defined within the individual subject space either by a knowledgeable neuroanatomist based on local anatomical landmarks [Nieto-Castañón et al., 2003] or through functional localizers acquired during the same session to define ROIs functionally [Kanwisher et al., 1997; Saxe et al., 2006; Fedorenko et al., 2010; Nieto-Castañón & Fedorenko, 2012]. These approaches may be better suited to high-resolution UHF-MRI studies where accurate alignment of functional areas across individuals is required.

Both approaches to ROI-based analysis are potentially simplified at UHF. Firstly, because of the pronounced anatomical contrast and higher spatial resolution of structural imaging, it is increasingly feasible to define meaningful anatomical boundaries in individual subjects based on microanatomical features [Sereno et al., 2013; De Martino et al., 2014; Dinse et al., 2015; Waehnert et al., 2016]. Secondly, the increased sensitivity of UHF-fMRI due to the boost in fCNR with field strength can translate into less time within an experimental session devoted to the auxiliary functional localizer scans, making them more practical than at conventional field strengths. Once the ROI is defined, the response amplitude or stimulus specificity may be compared within the ROI across individuals. When defining ROIs functionally, the experimenter must be careful to not derive the ROI using the same data that are to be compared [Kriegeskorte et al., 2009, 2010b; Vul et al., 2009]. In general, a distinct functional localizer can help to avoid this error. Even when a distinct localizer is used, it is important to define these ROIs using consistent criteria across individuals to help ensure that the region does correspond to the homologous area in all subjects. While some inter-subject variability is expected in certain brain regions, the functional localizer boundary can be inaccurate in any individual due to noise, so ideally a well-defined procedure for consistently choosing the boundary should be established.

Finally, many UHF-fMRI studies forgo formal group-level analyses and instead present detailed activation maps within individual subjects in each subject’s native space. In experiments mapping fine-scale functional organization, such as experiments investigating cortical columns, spatial normalization may not be accurate enough to align and compare the fine-scale patterns of functional activation across individuals, and so naturally in these cases single-subject analyses are mandatory. With the extra detection sensitivity provided by UHF-fMRI, it is possible to generate meaningful activation maps in individual subjects, and to examine the spatial characteristics of the maps at the individual level. An example of a recent single-subject study is shown in Fig. 6, where the individual finger digit representations are mapped within the human somatosensory cortex [Sanchez-Panchuelo et al., 2012]. With these maps, the cortical magnification can be characterized at the individual level, and potentially linked to a behaviorally-relevant measure within the individual [Duncan & Boynton, 2003].

Figure 6. Within-digit single-subject somatotopy.

(A) The somatotopic representations of the five fingertips within the postcentral gyrus displayed on a cortical surface reconstruction. An orderly progression of the five digits is clearly seen. (B) Fine-scale somatotopy mapped within the first finger using a traveling-wave stimulus (similar to phase-encoded paradigms) using high-resolution fMRI at 7T. (Reproduced from Sanchez-Panchuelo et al. [2012], with permission.)

A distinct challenge for these studies is to demonstrate the validity of the results by showing a sufficient number of example subjects. Many studies address the question of validity by showing the reproducibility of the derived activation maps within individual subjects across experimental sessions [Yacoub et al., 2008; Nasr et al., 2016], and a reproducible map helps to argue against the spurious maps arising from statistical noise. Because of the many sources of systematic errors that can persist across experimental sessions and can influence the appearance of these spatial maps, such as those due to large draining vessels on the cortical surface [Olman et al., 2007; Polimeni et al., 2010a], additional steps must be taken to ensure the validity of these maps at the individual single-subject level.

There are distinct advantages of single-subject study designs, even for studies investigating extended regions of activation across the brain. For clinical studies seeking to investigate brain function in individual patients to help identify disease from patterns of brain function, group-level studies may be inappropriate [Arbabshirani et al., 2016]. Comparing an individual patient to a normative database may help to identify disease patterns and classify patients [Zarogianni et al., 2013], but this requires sufficient detection sensitivity at the individual level. While the current generation of UHF scanners operating at 7 and 9.4T provides a substantial boost in fCNR compared to conventional clinical field strengths such as 1.5 and 3T, it is unclear whether there is sufficient detection sensitivity available today for such single-subject investigations. Nevertheless, the prospect of individualized fMRI analyses and the potential for fMRI-based diagnosis of neurological or psychiatric disease is a motivating factor for the continued development of single-subject study designs and analyses.

6. CONCLUSIONS AND FUTURE DIRECTIONS

In this review we have surveyed fMRI analysis strategies for UHF, with a focus on approaches for high-resolution studies. Particular attention was paid to strategies that preserve resolution by avoiding implicit or explicit smoothing of the data, mainly through anatomically-informed or surface-based analyses, to best exploit the benefits of small-voxel data afforded by UHF-fMRI. We also highlighted the different characteristics of the fMRI signal and noise that appear at higher field strengths.

Although there has been great progress towards UHF-fMRI analysis, several challenges remain. For example, surface-based analysis of fMRI data would benefit from incorporating progressive meshing schemes [Hoppe, 1996] to allow for specifying mesh resolution independently from anatomical voxel size; initial steps towards this have been taken by the Human Connectome Project analysis pipeline, the Connectome Workbench [Glasser et al., 2013] and by the AFNI SUMA package [Saad et al., 2004]. For high-resolution studies investigating small-scale brain organization, there is a need for tools that can enable the evaluation of sampling biases and resolution losses, especially as they vary within and across brain regions. There is also increasing need for accurate surface reconstruction from partial-brain anatomical data, which are acquired when using high-density localized array coils that are becoming increasingly available [Petridou et al., 2013; Farivar et al., 2016; Keil et al., 2017]. While the partial-brain data provided by these localized array coils introduce several challenges for certain automatic brain atlasing steps that necessitate whole-brain data, one can acquire anatomical reference data during a separate experimental session with a conventional array coil. Nevertheless, there is great potential for these localized array coils to provide immensely useful ultrahigh-resolution anatomical data. With recent demonstrations of the impact of structured physiological noise on multiple comparisons correction based on parametric statistical models [Eklund et al., 2016] and how these effects may be exacerbated at UHF [Wald & Polimeni, 2016], permutation tests with “spatially non-stationary” or spatially varying smoothness estimates [Hayasaka et al., 2004] may become mandatory for UHF-fMRI analysis.

Enabled by advances in high-resolution UHF-fMRI acquisition, the relatively recent possibility to sample fMRI signals across cortical depths—enabling investigations of laminar-level processing and connectivity—presents both opportunities and challenges, as outlined above. In these intracortical fMRI investigations, the cortical “sheet” is no longer treated as a two-dimensional surface but as a three-dimensional volume with a laminar organization. Both surface-based and voxel-based cortical-depth and laminar analyses can be employed, each offering distinct advantages and disadvantages. However, the key is that both approaches perform analyses in ways that respect the underlying functional and anatomical architecture: in surface-based approaches the representation of the laminar organization is explicit, while in voxel-based approaches the representation is often implicit. Regardless of the analysis approach, it is critical to be mindful of sources of sampling bias, detection bias, and resolution loss. While many of the recommendations offered in this review may be familiar to UHF-fMRI practitioners, to our knowledge there does not yet exist any fMRI analysis software package that integrates these strategies into a simple-to-use, robust pipeline that is broadly accessible to UHF-fMRI newcomers. There is a growing trend amongst popular MRI and fMRI analysis packages toward supporting high-resolution data [Glasser et al., 2013; Bazin et al., 2014; Lambert et al., 2014; Shafee et al., 2015; Zaretskaya et al., 2015], with analysis tools that can handle the distortions and noise sources present in UHF-fMRI data. It is our hope that the techniques and strategies summarized here, many of which may be considered advanced today, become more commonplace as software tools become available.

Of course, as more sophisticated and powerful analysis tools become available there is the potential for creating increasingly complicated analysis streams, perhaps in pursuit of marginal gains in statistical significance—a goal that warrants careful deliberation. Such processing streams are challenging to understand and reproduce and thus our opinion is that, whenever possible, simple and concise analyses should be favored. This strategy can help improve interpretability of the results, and can also aid in assuring comparability across research laboratories and institutions.

Today most UHF-fMRI studies typically utilize a small number of subjects, in part due to the limited availability of UHF scanners and the relative heterogeneity of scanner hardware across sites which preclude large-scale multi-institutional studies. Indeed some large-scale UHF-fMRI studies are beginning to emerge at advanced imaging centers [Uğurbil et al., 2013]. Recent developments announced by the major MRI manufacturers are also indicating that the next generation of UHF scanners will be more standardized across sites, and as these UHF scanners become more broadly available larger, multi-institutional studies may follow. The first generation of publicly-available data repositories of UHF-fMRI data have recently emerged [Forstmann et al., 2014; Tardif et al., 2016], which will hopefully facilitate future efforts into data sharing, but this availability of data also increases the demand for analysis tools appropriate for these data. At the same time, there is a growing need for single-subject study designs to facilitate fMRI studies looking at inter-individual differences in brain function rather than differences at the group or population level. While conventional power analysis may not be appropriate for designing a study comprised of single-subject analyses, some guidelines should be established for how many subjects should be required for publishing.

Overall, the increased resolution and the enhanced neuronal specificity afforded by UHF-fMRI is enabling new classes of fMRI experiments. Recent advances in UHF-fMRI acquisition technology have provided smaller voxels and faster sampling, and recent advances in UHF-fMRI analysis strategies can help to retain the benefits of these acquisitions and interrogate data in new ways to help UHF-fMRI come closer to its full potential.

APPENDIX

Matching the geometric distortion between two EPI acquisitions with different spatial resolutions requires evaluating the distortion in absolute units (e.g., millimeters) for each acquisition. The geometric distortion of EPI data along the phase-encoding direction, y, corresponding to a local magnetic field offset ΔB, is commonly expressed as

$$\delta y=\frac{\mathrm{\Delta }{t}_y}{{\tau }_{\text{pe}}}\frac{\mathrm{\Delta }B}{G_{\text{pe}}}$$ (1)

where Δt_y is the effective EPI echo spacing (i.e., the nominal EPI echo spacing divided by the in-plane acceleration factor R), G_pe is the amplitude of the phase-encoding gradient blip, τ_pe is the duration of the phase-encoding gradient blip, and δy is the resulting displacement or shift in the phase-encoding direction in units of meters. Typically this distortion is calculated in order to unwarp or distortion-correct the image, therefore it is often more convenient to evaluate the distortion in units of voxels [Jezzard & Balaban, 1995; Holland et al., 2010], but when comparing distortions in two acquisitions with different voxel sizes it is necessary to consider the absolute displacement in units of meters as in Equation (1). This displacement can be equivalently expressed in many ways in terms of various combinations of acquisition parameters, but one convenient equivalent expression is given by

$$\delta y=\frac{\mathrm{\Delta }{t}_y}{\mathrm{\Delta }{k}_y}\delta f\text{or}\delta y=\left(\mathrm{\Delta }{t}_y·{\text{FOV}}_y\right)\delta f$$ (2)

where τ_peG_pe = Δk_y/γ̄, FOV_y = 1/Δk_y, and γ̄ = γ/2π is the gyromagnetic ratio. This expression highlights that the displacement along y in units of meters is a function of both “temporal” parameter Δt_y (which is the time between blips during which distortion can accrue) and “spatial” parameter FOV_y (which is related to the strength of the EPI phase-encoding gradient blips). Therefore, for a given frequency offset δf due to local magnetic field inhomogeneity, the resulting displacement δy is given by the product of the FOV along y and the effective EPI echo spacing, (Δt_y·FOV_y). In the special case where the two protocols have the same FOV (and therefore the same phase-encoding gradient blip), the protocols will have matching distortions if the effective EPI echo spacing is set to the same value. Note that scanner manufacturers often provide the full bandwidth along the phase-encoding direction Δv_y given by Δv_y = 1/Δt_y, or the bandwidth per pixel along the phase-encoding direction Δv_y,_pp given by Δv_y,_pp = 1/(Δt_yN_y), where N_y is the number of phase-encoding lines [Holland et al., 2010], or fat–water-shift in pixels, which must be converted to frequency difference from the known difference between the chemical shifts of water and fat together with the magnetic flux density to be usable in one of the formulae above. The bandwidth per pixel corresponds to the frequency offset δf that would give rise to a geometric distortion whose displacement would be one voxel length, e.g., if the bandwidth per pixel for a 2×2×2 mm³ protocol were 400 Hz and locally the magnetic field inhomogeneity resulted in a 200 Hz offset the voxels would be locally displaced by ½ voxel or 1 mm. However, the more relevant quantity for comparing phase-encoding bandwidth across different acquisition protocols is the bandwidth per meter Δv_y,_pm given by Δv_y,_pm = Δv_y,_pp/Δy = 1/(Δt_y·FOV_y), where Δy is the voxel size along the phase-encoding direction. The bandwidth per meter Δv_y,pm is the same term expressed in Equation (2) that relates the local magnetic field inhomogeneity to the pixel displacement along y.

While most geometric distortion in EPI appears along the phase-encoding direction, which has the lowest bandwidth of all three spatial encoding directions, for high-isotropic resolution acquisitions slices can sometimes require reduced bandwidth of the slice-selective RF pulse, and the large magnetic field inhomogeneity at ultra-high fields can cause a noticeable amount of geometric distortion in the slice direction as well. Similar to the distortion in the phase-encoding direction, distortion in the slice-encoding direction can be matched between the functional EPI acquisition and the anatomical EPI acquisition even in cases where the two acquisitions have different voxel sizes or different slice thicknesses [Błażejewska et al., 2017]. For distortion in the slice encoding direction, the shift along z in units of meters is given by

$$\delta z=\frac{{\text{FOV}}_z}{\mathrm{\Delta }{v}_z}\delta f$$ (3)

where Δv_z is the bandwidth of the slice-selective RF pulse. In this case, since there is only one pixel along the slice-encoding direction, this bandwidth is equivalent to the full bandwidth as well as the bandwidth per pixel, and the FOV_z is equivalent to the slice thickness Δz. Therefore, as with the phase-encoding distortion, ensuring the same slice-encoding distortion requires matching the term FOV_z/Δν_z between the functional EPI and anatomical EPI protocols, e.g., for a 0.8 mm functional EPI protocol and a 1.0 mm anatomical EPI protocol the slice-encoding bandwidth for the anatomical EPI protocol must be set 1.25 times higher than the slice-encoding bandwidth used for the functional EPI protocol.